Alright, but there still exists a difference between something that convinces someone and evidence. Jenny McCarthy is "convinced" that autism is caused by vaccines, but the thing that convinces her is a mere correlation, not evidence (and persists in her position even when presented with evidence that suggests otherwise!).
Historically, then, what is evidence?
For a great deal of ancient history, the evidence we have is documents -- and nothing else. That's all we have to tell us there ever was such a person as Socrates; how do we know he wasn't a figment of Aristotle's imagination, invented for some reason of his own? For that matter, what evidence do we have for Aristotle, save the words of others?
In historical terms, we have more certainty about the life of Jesus of Nazareth than we do about either of those Greek thinkers, yet we take them as fact, while many dispute even his existence! The documents attesting to his life are much closer in time (less than a generation away, for the first) than those for the two aforementioned Greeks, yet how many people claim they never existed?
And to many scientists, the universe is filled with evidence of a Creator -- so I have to wonder if what's at issue here is a subjective determination of what constitutes "evidence".
And what would be the demonstrated record of, say, the Biblical God existing but not Zeus or Poseidon? I'm sure Christian believers trust that the former is true, but I'm not sure if it is based so much on a "demonstrated record" as it is indoctrination or a susceptibility of superficial, convincing events (like MikeyLove who admitted to have been convinced when an earthquake came to pass and the [strike]flag was still there[/strike] picture of the Immaculate Heart of Mary was still on the wall when all the other nick-nacks fell). I'll give you the benefit of the doubt that you're more "sophisticated" than he is, though I'll hold my breath till presented with evidence.
We've been over that: documents written by people who were alive when Jesus was, vs. (as noted by someone in this thread) tales rarely taken as actual even by those who 'believed' in the Greek gods.
And as I've explained previously, none of the Greek gods really stands up to real qualifications for godhood; they are gods in a much watered-down version of the robust vision the Bible presents of a Creator who isn't tangled up in the created, who didn't emerge from the created, but who is prior to it all and sustains it all moment by moment.
As for personal evidence:
I was once in a gathering where "speaking on tongues" took place, and experienced receiving a translation/interpretation. I know that's what it was, because I chickened our when the pastor asked (as Paul directs) for an interpretation, and what the guy who actually spoke up said differed from what I'd 'heard' only in the ways that one Greek student's translation of a passage in Xenephon might differ from another -- and then others provided affirmation that they had understood it the same way as well.
I've also experienced what the Bible calls "word of knowledge".
Since these were things I hadn't sought, and wasn't terribly comfortable with, and corresponded to the Bible's description, and since there is no convincing explanation from any other source....