When is "this day"
As you rightly note, Psalms 2:7 is quoted multiple times throughout the new Testament. Clearly this had special significance to the New Testament audience. One reason for this can be seen in verse 1 which reads:
ἵνα τί ἐφρύαξαν ἔθνη καὶ λαοὶ ἐμελέτησαν κενά (LXX)
לָמָּה רָגְשׁוּ גֹויִם וּלְאֻמִּים יֶהְגּוּ־רִֽיק׃ (MT)
Why do the nations rebel? Why are the countries devising plots that will fail? (NET)
Why have the Gentiles raged, and the people devised vain things? (DRA)
Why do the heathen rage, and the people imagine a vain thing? (KJV)
Each of these translations was chosen to illustrate an important point about the range of this word. In Hebrew גֹויִם transliterates to goyim, or gentile. Modern Jews have been known to even employ a Shabbos goy ("Sabbath Gentile") to do work like lighting fires or stoves and turning on lights and similar activities forbidden by Jewish law and customs. This is why the translators of the Douay-Rheims Bible chose "Gentiles" for their translation. In greek, ἔθνη means foreign nations (Which is why the NET chose "nations" for their translation) or foreign peoples (ἔθνη transliterates to ethnos, the origin of the English word "ethnic" and "ethnicity"). As you can imagine, this mainly became a pejorative shorthand for the Roman Empire during New Testament times, as the Roman Empire were the foreign people Israel. As such, the KJV chose "heathen" which tends to capture the pejorative nature of this term.
Accordingly, the BDAG1 notes:
Sometimes it is plainly Hebrew influence which gives special meaning to words and expressions in the LXX and our literature. τὰ ἔθνη = ‘the heathen, Gentiles’ comes about when that plural form is used to translate גּוֹיִם, a rendering that was more natural for the translators of the LXX, because among the Greeks it had become customary to call foreigners ἔθνη
And on Pg 276, the BDAG defines this word as meaning:
People groups foreign to a specific people group (corresp. to Heb. גּוֹיִם in LXX; a nationalistic expression, also usually in Greek for foreigners.
those who do not belong to groups professing faith in the God of Israel, the nations, gentiles, unbelievers (in effect=‘polytheists’)
So, this is a somewhat coded signal to the New Testament reader that the "begetting" occurs during the day that the Gentiles/Romans/foreign peoples rage and devise plots doomed for failure; the time when kings of the earth form a united front and collaborate against the LORD and his anointed king.. Essentially, the New Testament authors are implying that "this day" refers to the time of the Roman Empire.
This then also ties into the theme of the expectation that the Messiah would be a militaristic leader who would come to overthrow the Roman Empire when we look at Psalms 2:8-9 (an expectation that persist even until today among Jews:
Ask me, and I will give you the [gentiles/foreign] nations as your inheritance,
the ends of the earth as your personal property. You will break them with an iron scepter; you will smash them like a potter’s jar!’”
Not "Begotten" but "Begat"
It is important to distinguish between the "firstbegotten", "begetter" and the "onlybegotten". In Greek and Hebrew the firstborn (πρωτότοκον / בְּכוֹר) recieves a birthright (πρωτοτόκιά / בְּכוֹרָה) from the father, the "begetter" (γεγέννηκά). When there is only one child born to a father, he is regarded as "onlybegotten" (μονογενοῦς)
Psalm 2:7 in the LXX, Acts 13:33 and Hebrews 1:5 all use the word "γεγέννηκά" which means to become the parent of. In it's masculine form, it refers to the father becoming a father and the feminine form refers to a mother giving birth. In other passages, Jesus is characterized as receiving a (πρωτοτόκιά / בְּכוֹרָה / birtright) from the father, but in these cases the word used only encapsulates the begetter.
The Athenasian Creed is heavily influenced by the Nicene Creed which has very similar wording:
We believe in one God, the Father Almighty, Maker of all things visible and invisible. We believe in one God, the Father Almighty, Maker of heaven and earth, and of all things visible and invisible. And in one Lord Jesus Christ, the Son of God, begotten of the Father [the only-begotten; that is, of the essence of the Father, God of God,] Light of Light, very God of very God, begotten, not made, being of one substance with the Father
Wikipedia characterizes Athenasius of Alexandria, the author of the Athenasian Creed as a "famous defender of Nicene theology" and goes on to state:
The Athanasian Creed uses the term substantia (a Latin translation of the Nicene homoousios: 'same being' or 'consubstantial') not only with respect to the relation of the Son to the Father according to his divine nature, but also says the Son is substantia of his mother Mary according to his human nature.
As you can see, it is pretty obvious that this earlier creed is the basis for the Athenasian Creed. While the Athenasian Creed is in Latin, the Nicene Creed is in Greek, and in fact uses the same Greek word γεγέννηκά as is used in Acts 13:33, Hebrews 1:5 and Psalms 2:7 LXX. So, in short, Yes; this is the same begetting as is referenced in the Athenasian Creed.
In contrast however are John 1:14 and John 3:16 which both use the word μονογενῆ (monogenē) or μονογενοῦς (monogenous)
On Page 658, the BDAG1 defines this word as meaning
① pert. to being the only one of its kind within a specific relationship, one and only, only
In one example given for the parent-child relationship in the BDAG, this term is used to describe Isaac as Abraham's only (legitimate) son in Hebrews 11:17.
The BDAG also notes that μονογενοῦς can:
② pert. to being the only one of its kind or class, unique (in kind) of something that is the only example of its category
So one example given is
Of a mysterious bird, the Phoenix 1 Cl 25:2
The BDAG also notes that one variant or usage of the word
μονογενὴς υἱός is used only of Jesus.
While this wording or sense of "onlybegotten-ness" does make it into the Nicene Creed, it doesn't seem to have "trickled down" to the Athenasian Creed.
Revelation 1:5 however uses the term πρωτότοκος (prōtotokos). This term refers specifically to the individual, as opposed to the blessing itself. The BDAG however does note on Pg 894 that this can and is often used figuratively to indicate
having special status associated with a firstborn
Again, while this concept of Christ as "firstborn" did not make it into the Athenasian Creed, it was reflected in the Nicene Creed.
Who inherits in Psalms?
In the Psalms, the authorship is traditionally attributed to King David. This can be seen in the title in Chapter 3 of Psalms, for example which states
A psalm of David, written when he fled from his son Absalom.
These titles appear in many older manuscripts and are generally understood to be a reliable attribution.
Thus, in Psalms 2, the "Day" that the author was referring to was the times of the reign of David and it was David himself who "begotten". By virtue of being the son of God, David is entitled to a birthright (πρωτοτόκιά / בְּכוֹרָה), the Covenant made to Abraham, Isaac and Jacob.
Inasmuch as the New Testament authors are drawing on this to use the "day" to refer to the times of Roman occupation, the attachment of this text to Christ indicates that it is Christ who is "begotten".
This duality is intentionally done in order to draw on the link of Jesus to the Lineage of David. The requirement that the Messiah be descendant of David can be seen in in Isaiah 11:1:
A shoot will grow out of Jesse’s root stock, a bud will sprout from his roots.
And also in Jeremiah 23:5-6:
“I, the Lord, promise that a new time will certainly come when I will raise up for them a righteous branch, a descendant of David. He will rule over them with wisdom and understanding and will do what is just and right in the land. Under his rule Judah will enjoy safety and Israel will live in security. This is the name he will go by: ‘The Lord has provided us with justice.’
And Jeremiah 33:17:
For I, the Lord, promise: “David will never lack a successor to occupy the throne over the nation of Israel.
Quoting Psalm 2 intentionally draws readers to Matthew 1:6 and Luke 3:31 which establish Jesus as a descendant of David. By virtue of being an heir of David, Jesus inherits the same birthright (πρωτοτόκιά / בְּכוֹרָה) that David inherits in Psalm 2.
Theologians like Dr. John F. Walvord term this the Davidic Covenant and teach that these verses indicate that through Christ, Jesus inherits and fulfills the original Covenant and establishes a "New Covenant" at the Last Supper.
For example, in the IVP New Testament Commentary Series, Theologian Ray Stedman states2:
The writer here especially claims the superiority of Jesus over the angels as the Son of Man. No angel could claim either eternity or resurrection as the basis of his sonship, but Jesus had both. Though the angels collectively were called sons of God, no individual angel ever is given that title, or singled out as having a unique status before God. So the writer demands rhetorically, To which of the angels did God ever say, “You are my Son; today I have become your Father”?
Psalm 2 is specifically applied to Jesus in Revelation 12:5 and 19:15 and to those who share his kingdom reign in Revelation 2:27, especially in conjunction with the words “you will rule them with an iron scepter” (Ps 2:9). Several scholars have felt that Psalm 2 represents a coronation liturgy which was included in enthronement ceremonies of the Davidic dynasty. One of the rabbis in Midrash Tehillim says of Psalm 2:7, “And when the hour comes, the Holy One—blessed be He!—says to them, I must create him a new creation, as it is said, ‘This day have I begotten thee.”’ Of this F. F. Bruce says, “The implication here seems to be that Psalm 2:7 refers to the time when Messiah, after suffering and death, is brought back to the realm of the living” (1964:13, fn. 63). This understanding would agree with Paul’s use of Psalm 2:7 in Acts 13:33 and clearly the word today refers to the resurrection of Jesus rather than the day of his birth in Bethlehem, or of his baptism in the Jordan.
The second source of support from the Old Testament draws on 2 Samuel 7:14. Historically the words “I will be his father, and he will be my Son” were spoken to David concerning Solomon when the prophet Nathan told David that Solomon will build a house for God in Jerusalem. There is, however, a hint that David’s power would extend to his progeny, which would also include the Messiah. The prophets in later times spoke often of a greater son of David who would fulfill all the promises to David of an eternal reign. Bruce quotes from the Dead Sea Scrolls where 2 Samuel 7:14 is linked with an expectation of the imminent restoration of David’s house by the “shoot of David,” the Messiah (1964:14). Note again how the human nature of the Lord is underscored by his title Son of David. As the risen Man, he claims the throne of David, but as such the Father calls him “my Son.” By these two quotations, with their royal implications, the writer of Hebrews claims that being related to God as a Son is a far greater title than any angel could claim. This rests on the base of a shared eternity and a resurrection, which is the “new creation.”
Similarly, Bruce Barton notes in the Life Application Bible Commentary on Hebrews3:
For to which of the angels did God ever say, “You are my Son; today I have become your Father”? Or again, “I will be his Father, and he will be my Son”? NIV Beginning here in 1:5 and continuing through 1:13, the writer strings together seven quotations from the Old Testament: (1) Psalm 2:7, (2) 2 Samuel 7:14, (3) Deuteronomy 32:43 (v. 6), (4) Psalm 104:4 (v. 7), (5) Psalm 45:6–7 (vv. 8–9), (6) Psalm 102:25–27 (vv. 10–12), (7) Psalm 110:1 (v. 13). All but two are found in the Greek Psalter, the hymnbook of the synagogue and early church. The writer introduces two quotations from the Psalms by asking the rhetorical question, For to which of the angels did God ever say…. The answer is, of course, he never said this to any angel.
The first quote, You are my Son; today I have become your Father, comes from a coronation psalm. Psalm 2:7 was also quoted at Jesus’ baptism (Mark 1:11) and transfiguration (Mark 9:7), as well as in 2 Peter 1:17. The psalm was originally sung at the crowning of a new king (perhaps originally of David or Solomon). This psalm was used for centuries of Jewish history as a song of worship. Jewish rabbis attached a deeper meaning to the song—one that looked forward to the coming Messiah. Because the Messiah fulfilled the promises of the Old Testament, the writer understands that these Old Testament verses apply to Christ. The present tense, “you are” (ei su), describes a continuing relationship. Jesus did not become God’s Son but was always God’s Son. The Father acknowledged him as his Son in a special way when Jesus was enthroned on high. The Bible calls angels “sons of God” (Job 1:6; 2:1), but not the Son of God. No angel or person other than Christ could ever receive that honor. There are two common interpretations for the word “today”: Either it could refer to Christ’s glorification (he has been elevated, honored, and seated at the right hand of God), or this honor was based on Jesus’ death and resurrection. The first choice is preferable because it continues the thought that Jesus is at the right hand of the Father.
God spoke the words, I will be his Father, and he will be my Son, to David with respect to Solomon (2 Samuel 7:14; 1 Chronicles 17:13). Although Solomon fulfilled these words, Hebrews illustrates that Christ ultimately and completely fulfilled them. In John 7:42, the religious leaders discussed Jesus’ authority, and they alluded to this passage in Samuel, which said that the Messiah must come from David’s family. The titles of “Father” and “Son” reveal a distinction between these two members of the Godhead. They also reveal the unique relationship of the Son to the Father. Although a unity exists in the Trinity, a distinction between the members exists, too. The question implies that no angel can claim such a relationship.
This day, as it is used in the New Testament refers to the time of the Roman Empire and specifically to Christ's resurrection. It is connected to Jesus being called God's son because Jesus is established as Heir to the throne of David and "begets" the birthright of the "Eternal Reign" promised to David, Solomon and his Heirs by the Prophet Nathan in the Davidic Covenant in 2 Samuel 7:14 and by later prophets. Referencing Psalm 2, a psalm used during coronation ceremonies is intended to signify Jesus coronation as "King of Kings".
It is a basis for the claim of being "begotten" in the Athenasian and Nicene Creeds along with a body of other passages.
1Arndt, William ; Danker, Frederick W. ; Bauer, Walter: A Greek-English Lexicon of the New Testament and Other Early Christian Literature. 3rd ed. Chicago : University of Chicago Press, 2000
2 Stedman, Ray C.: Hebrews. Downers Grove, Ill., U.S.A. : InterVarsity Press, 1992 (The IVP New Testament Commentary Series), S. Heb 1:6
3 Barton, Bruce B. ; Veerman, David ; Taylor, Linda Chaffee ; Comfort, Philip Wesley: Hebrews. Wheaton, Ill. : Tyndale House Publishers, 1997 (Life Application Bible Commentary), S. 8