You really do not understand, do you? You really do not know the significance of the Bethlehem birth story and why Matthew and Luke have to get him born there, though they go about it in two irreconcilably different ways? You really do not understand why the later Synoptics have to jump through such hoops, as TimCallahan says, to get a Galilean born in Bethlehem, a most improbable circumstance? And how the birth stories, absent from Mark and John, can't possibly be true? So if he has to be born in Bethlehem, it would suit Matthew and Luke better to state that he was really from Bethlehem, and always lived there. Why then do we keep getting told he was a Galilean? Is it because he really was one, and the evidence for that is ineluctable?
This is the sort of argument I offered earlier, in the post you won't read, about Jesus' baptism by John, another embarrassing story that the later gospels would like to omit, but they can't. Why can't they? Because it really happened? Can you see the force of arguments of that kind? They may be wrong, but they depend in no way on the assumption that the NT is infallible, or any such rubbish.
The Bethlehem clue, by the way, is in John 7:41-43 The Scripture that says it is Micah 5:2 Yet he is located in Galilee as John points out. Why? Well a very parsimonious way of explaining this is to suggest that a mythical Jesus was born in Bethlehem for ideological reasons, and the one resident in Galilee is a real one. Is that an insane idea? No. Does it depend on the infallibility of the gospels? No.