There isn't a way (as far as I can tell) to prove that God does or does not exist. Jesus DID exist. There were thousands of eye witnesses who actually saw him.
I think the hypothetical you propose is interesting but impossible. However if you'd like to talk to people who believe in things that never happened, just find yourself a Scientologist and ask them about Xenu!
No it isn't impossible.
The only proof you have of Jesus even existing is supposed eyewitness accounts written by people third or fourth hand down and who were definitely not there. There is no physical proof Jesus existed.
Regardless, your faith is your faith. My question is what happens if you find what you believed in isn't the truth. What if James Cameron is right?