About the existence thing, the existence of a random normal person in history is relevant. If you live your life without claiming to be a messenger from god to tell about eternal life, secrets of universe, etc, you don't have to prove nothing about your existence to the future generations.
But what about a supposed superman on earth?
What about if you can ressurect a person but can't write something in a kind of magical time resistant paper or vellum?
If we have a vellum of graphene with a LCD screen from 2000 years ago I would bet some coins in this tale.
He ressurected a man!
Extraordinary claims needs extraordinary proofs.
When you have extraordinary claims with no extraordinary proofs the doubt must be default.