I think the first question to ask is, what kinds of claims can science test? The only evidence for a virgin birth comes form the Gospel of Matthew and Luke. If we were there at the time, with a pregnant Mary what could we even prove? You can certainly test if someone was a virgin and pregnant at the same time. Anyways, you get the point. DNA tests on the baby? Joseph's not the father?
You can certainly test someone's claims if they have any kind of physical evidence (i.e. there was not a global flood that killed everything 4,000 years ago). One interesting example is found in the Old Testament with the prophet Jeremiah who is recorded as saying (Jeremiah 32:6-8):
6 Jeremiah replied, “The word of the Lord came to me: 7 Watch! Hanamel, the son of your uncle Shallum, is coming to you to say, ‘Buy my field in Anathoth for yourself, for you own the right of redemption to buy it.’ 8 “Then, as the Lord had said, my cousin Hanamel came to the guard’s courtyard and urged me, ‘Please buy my field in Anathoth in the land of Benjamin, for you own the right of inheritance and redemption. Buy it for yourself.’ Then I knew that this was the word of the Lord.
Here's the guy who apparently could have been put to death for wrongly prophesying, but yet wasn't sure about God speaking to him until the thing he heard came to pass. That certainly is an interesting way to move forward with faith claims.
However, perhaps you might more generally be wondering, God where are you in all this? In which case I think this article also you might find interesting: