Well, currently, "birds" are pretty much defined as "Archaeopteryx and its descendants," because it's the only fossil of its "type" to have the characteristics of birds that are necessary to indicate common descent to all modern birds. Other theropods had similar features (such as feathers), but they lacked the other features necessary to indicate a relation to modern birds (the toe being the best example).
I think it's likely that we will never know for sure because the fossil records are so incomplete. I'm sure someday in China we will unearth the true first bird and not even know it.
And of course by nature the fossil record is incomplete, but then our picture of the different branches of descent comes (in part) from what we actually have of the fossil record. It's always possible that new discoveries will revolutionize the field or disprove currently-understood models, but that's nothing to worry about, as it happens all the time and is an expected part of the process. We don't make radical changes to our arrangements based on what could happen, but rather what does happen; and so if we do make such a discovery, then we will have to change the model accordingly, but until then we have a model that's also soundly based on current evidence.
For all the things that I never did
For all the places I never was
For all the people I never stopped
But there was nothing I could do..."