What proof would you require of the existence of a deity whose characteristics included at least omnipotence and omniscience among others?
A clearer definition. What sort of deity are we talking about here? (Heck, when you get down to it, what's a deity?) Would a sentient cluster of stars count? Maybe a really tall Greek guy with an enormous wang?
If we're just talking about a creator of the universe, then I guess the first thing I'd need is a description of what, exactly, the thing we're supposed to be looking for is, and how, exactly, it went about the process of creation.
What proof would you require of the existence of any deity whose existence has already been specifically postulated via any specific religious text or creed?
Depends on the religion. Although as far as I know, none of them have gotten very specific in their postulating.
"We had survived to turn on the History Channel
And ask our esteemed panel, Why are we alive? And here's how they replied:
You're what happens when two substances collide
And by all accounts you really should have died."
-Andrew Bird
™ Version 4.2