As Douglas Adams put it, and rather ironically as he was an atheist, G-d exists on faith and proof denies faith and therefore G-d cannot be proven. Man goes on to posit that the grandeur of the world proves He exists and therefore by His logic, He doesn't and goes poof.
It's a good point though. The search for proof is a search for knowing. That which you know, you have no need of faith in. I know my chair is under my ass. I have no particular faith in my chair. I have no knowledge whatsoever that my wife will find a job in her chosen field. I have faith that she will.
It isn't even that the analogue to proof is belief. It's not. It's suspension of disbelief. You can believe whatever you want. It's when you start to not believe in a specific thing that you head towards proof being needed to establish bonafide knowledge.
Let me give you the example of Star Trek. You don't know that it is real or not, but you have a lot of proof that it isn't. But you choose to suspend disbelief, the process of rejecting faith and instead requiring proof because the lack of knowledge discomfits you. In doing this, suspending disbelief by free will, you can in your mind accept that Captain Kirk is real in that assumption that he is, and get on from there to wishing you were snogging with the green Orion slave girl.
Why do we find it easier to suspend disbelief to "get into" the adventures of fictional people, and yet find it so hard to maintain faith in G-d?
Shabbat Shalom all.