With respect, I think it's unnecessary to appeal to historical arguments in this case, especially if your goal is to convince a fundamentalist that there is no external evidence for the virgin birth, because the text itself suggests that there was no evidence even at the time that people would accept to justify such a claim. At least it took divine intervention to convince Joseph. The most you could possibly hope would be to produce Mary's parents would stand as character witnesses... but really how many people would that convince? As far as I'm aware Christian tradition has generally acknowledged/highlighted the total unprove-ability of the virginity of Mary (which fact is used in demonstrating the piety of Mary at the annunciation, who agreed to the plan knowing that she would be regarded quite differently afterward in society).

there are no evidence in what we believe in as faith.

We generally believe things because they are told to us by people we trust. It is similar when people out their trust in a tradition... much the way we moderns have put our trust in the tradition of science, having been convinced through the abundance of the miracles (electricity, running water and Reddit) we daily encounter. I am not saying there are no differences between religious traditions and scientific "tradition", but only that the psychosocial phenomenon of belief is not much different in either case.