JRafael:
The Bais Halevi at the end of Bo says that it is impossible to prove Yiddishkeit to a person who has lost his emuna.
He explains there that all the debates that took place with chaza”l were to disprove anything that disproves Judaism. But to positively prove Judaism is impossible.
I understand this to mean that there is nothing that disproves Judaism but there is also no empirical evidence to prove it.