There’s a very simple explanation: free will.
If there were “proof” (in the mathematical sense–no one denies 2 + 2 = 4, for example) then everyone would be compelled to believe. There would be no free will.
To repeat an example I’ve given before, what if you could buy a genetically modified dog that would love you no matter what? Would this be preferable to a dog whose love would be conditioned by how you treated the dog? I think all of us would rather have a dog whose love has to be earned. It’s always iffy to anthropomorphize God, but I would think God feels the same way. If you “have” to believe in him, it’s not as good.