Let me take a quick stab at it. Would like to start-off with a counter question? "what would prove God's existence" ? Miracles?
To me, God IS Existence, it doesn't require a proof...Now, if the mind requires a logical proof with a language, that would be a hard-sell because God is beyond the mind. The purpose of pretty much all medicational practices is to go beyond the mind. For example, the difference between a living body and a dead body is presence of life energy, which makes everything work.. This life energy is called by different names, soul, consciousness etc. Hope that helps.
The debate between atheists & believers is ancient and continues to this day!! It has never gotten anywhere! Every argument broken by a different argument, spiced by trading insults & taunts!!
Check out the heated debate between Deepak Chopra vs Sam Harris , regarding the existence of God :) :)