establishing that God even exists
You got it all wrong. That’s what the Bible is all about: “They will have to know that I am Jehovah.” And that is what Christianity is about: “They will see, the Son of Man.” “Every eye will see him.” and the vindication of his church. That is miraculous proof from God which man cannot provide. Not like the miracles recorded in the Bible as evidence that Jesus was the Messiah —-which the Jewish nation rejected. But the sort of evidence that the Bible refers to as:
“in a flaming fire, as he brings vengeance on those who do not know God and those who do not obey the good news about our Lord Jesus.” —But that is not what this Forum is about. I am only replying to your question from the Bible. The proof that you seek cannot be provided by me.