Opposing reason and faith is a category mistake. Most of what we think we know we actually believe. No one can personally verify every fact they've been taught or that they accept to be true.

That said, whether Jesus of Nazareth existed or not is a historical question, not a religious one. Whether he is all that is claimed for him is indeed theological, but one thing Christian theologians have finally agreed upon is that Jesus is/was as human as you or me.

Which brings us back to the question of his existence as a human, a man, a Jew. There is other evidence you do not mention, but Paul Zanki's comment below gets to the heart of the matter of what is historical or not. By the way, ancient authors were very attached to eyewitness testimony...