There is a problem with the notion of proving God exists.
An existence is presumed without proof.
Existence, what ever that means, exists.
Why would existence need God?
I agree.
Existence is something I would consider as proof or evidence (Paul speaks of God being made known through Creation as self evident - we all know it, and we all deny this truth until we come to Him in Christ).
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. For what can be known about God is plain to them, because God has shown it to them. For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. For although they knew God, they did not honor him as God or give thanks to him, but they became futile in their thinking, and their foolish hearts were darkened. Claiming to be wise, they became fools, and exchanged the glory of the immortal God for images resembling mortal man and birds and animals and creeping things.
~ Romans 1:18-23
The problem with the notion of "proving God exists" Existence does not need the proof, God does. Besides what ever is contingent upon existing is not God. Things in existence are contingent on God.