If God wanted to be 'provable', we wouldn't we have anything left to prove (it would already be proved...). The option to doubt (or to believe) the existence of God, leaves an opportunity for love. Choice is essential to love. If we saw God, we would lose that choice. Though it's interesting to attempt to prove God; I'm currently reading "The Physics of Christianity" [0]. I can't say I stand behind it completely, but it's a fascinating effort.

[0] - https://www.amazon.com/Physics-Christianity-Frank-J-Tipler/d...