This is one of the most commonly asked questions and deserves an honest answer. Below is first a short answer then a more thorough answer. There are three things we need to consider when answering the starlight question.
1. Scientists cannot measure distances beyond 100 light years accurately.
2. No one knows what light is or that it always travels the same speed throughout all time, space and matter.
3. The creation was finished or mature when God made it. Adam was full-grown, the trees had fruit on them, the starlight was visible, etc.
Let me elaborate on these 3 points.
First, no one can measure star distance accurately. The farthest accurate distance man can measure is 20 light years (some textbooks say up to 100), not several billion light years. Man measures star distances using parallax trigonometry. By choosing two measurable observation points and making an imaginary triangle to a third point, and using simple trigonometry, man calculates the distance to the third point. The most distant observation points available are the positions of the earth in solar orbit six months apart, say June and December. This would be a base for our imaginary triangle of 186,000,000 miles or 16 light minutes. There are 525,948 minutes in a year. Even if the nearest star were only one light year away (and it isnít), the angle at the third point measures .017 degrees. In simpler terms, a triangle like this would be the same angle two surveyors would see if they were standing sixteen inches apart and focusing on a third point 8.24 miles away. If they stayed 16 inches apart and focused on a dot 824 miles away, they would have the same angle as an astronomer measuring a point 100 light years away. A point 5 million years away is impossible to figure with trigonometry. The stars may be that far away but modern man has no way of measuring those great distances. No one can state definitively the distance to the stars. The stars may indeed be billions of light years away, but man cannot measure those distances.
Several other methods such as luminosity and red shift are employed to try to guess at greater distances but all such methods have serious problems and assumptions involved. For a more complex and slightly different answer to the star light question from a Christian perspective, see the book Starlight and Time by Russell Humphry available from www.icr.org.
Second, the speed of light may not be a constant. It does vary in different media (hence the rainbow effect of light going through a prism) and may vary in different places in space. The entire idea behind the black hole theory is that light can be attracted by gravity and be unable to escape the great pull of these imaginary black holes. No one knows what light is let alone that itís velocity has been the same all through time and space. Since atomic clocks use the wavelength of the Cesium 133 atom as a standard of time, if the speed of light is decaying, the clock would be changing at the same rate and therefore not be noticed.
Third, the creation account states that God made light before He made the sun, moon, or stars. The rest of creation was mature, so starlight was probably mature at creation as well. I would ask the question, How old was Adam when God made him? Obviously he was zero years old. But how old did he look? He was a full-grown man. The trees were full-grown with fruit on them the first day they were made. The creation had to be that way; it would not work otherwise. Stars and their light were made at the same time. The God that I worship is not limited by anything involving time, space or matter.