Amazing.
Every atheist, agnostic, ignostic, believer or non believer here has pretty much defined who or what God must be, what He must look like, what She must act like, what It must be capable of. Once God is properly defined in the imagination of the ag/ig/atheist or theist, then the possible encounter is scripted...and found to be impossible. There. All done, God doesn't exist so if He showed up in the defined iteration, that would be proof that he didn't, and if he does NOT show up as defined, well, that also would be proof that the experience was "not God,' 'more gravy than of grave'
non believers would not accept any evidence of God...especially objective evidence, since of course they have already decided that there can not be any objective evidence of God. How can there be? He doesn't exist.
Circular indeed, but I've never met an atheist who SAW the circularity of it.
I suggest, humbly, that the non believer stop attempting to put this God he doesn't believe in into a box for comfortable definition. He won't fit there.
Just....be. If God wants' to prove Himself to you, He will.