The trouble with asking about a proof of God’s existence starts with him who makes the demand, because he must tell us first what he expects of a proof. A proof in mathematics proceeds in one way, in history, another and in law, yet another. What counts as “evidence” in one domain is not evidence in another. So, before challenging the believer to prove what he believes, make clear what you mean by “proof” because you may very well be asking for what cannot be given, not because a proposition is unprovable, but because your understanding of proof is skewed.
Here’s how tricky proofs can be. Let us start with simple perception. How do I know that there is an iPad in front of me? That is, of course, a matter of perception, but I can be misled, as dreams, illusions and mirages more than amply establish. So, I check once more: I look, I touch, I click the iPad on and off to hear the sound it makes, and if I am so minded—and so desperate—I may lick it. Still unsatisfied, I may call others to my room to ask them what they see in-front of me. When they assure me that there is an iPad in front of me, that should do it. Then, for all purposes I can declare with certainty; “There is an iPad in front of me.” But is that declaration absolutely immune from doubt? Not really. But the point is that to ask for immunity from all doubt is to ask for what is unattainable. That is not just the nature of human knowledge, and certainly, not the nature of perception. In short, when all reasonable questions have been answered, then that should suffice, and I should be able to maintain “without a doubt” that there is an iPad in front of me. See, what a tricky business “proving” is?
Now as for God, the classic proofs of Thomas Aquinas known as the “quinquae viae” (S.T. I, Q. 1, A. 3) are there —but, and here is the important point—they are good only if one seeks an explanation of what presents itself to experience. But if one says: I do not need an experience of motion (change), of causality, of what comes to be or ceases to be, since I take these as final and ultimate givens, then the proofs do not work.
In the end, it is a matter of “seeing as”—and there are enough examples of this other than God. Is it a goblet or a face? Is the misery of another person any matter to me or not? (That is the ethical level of “seeing as”). One can look at the fact that evolution has moved in crooked lines but without a doubt towards the production of ever higher levels of intelligence. There is also the fact that for all our remaining savagery, we are realizing that we ought to be kinder to each other in so many respects. There is a drive towards ethical goodness. Even the whole LGBT issue is an indication of our increasing sensitivity to the demand of “being good”—no matter that many protest the obscurity of the concept. One can see this all AS the Divine that is at work in the universe, or one can dismiss it all as happenstance.
So “God exists” and “God does not exist” are choices of interpretation, with reasons to support each, but they are not equal choices, because while the affirmation of God allows so much to be explained that would otherwise be unexplained, the denial of God leaves the whole ensemble of things an ultimate, inexplicable given!
So, yes, there is proof—there is reason to say that God exists, but there is also a choice to be made. That gap that choice fills in, that is called “epistemic distance.”
And if you think that that is a weakness of the “proofs of God’s existence,” epistemic distance is not a weakness. It is a feature of human cognition. Is the person I love truly loving or merely deceiving me—the ultimate lover’s dilemma. Some prefer not to face it and just to love. That might be the best thing to do. But the fact is that when one goes over the “proofs,” one will have some items listed “for” and items listed “against.” In the end, one must make a choice, and it will not be an irrational leap, but neither will it be one absolutely immune from the assaults of doubt.