If God cannot prove His omnipotence (or infinity) to human beings because they are neither omnipotent or omniscient or infinite, couldn’t God simply make all human beings into omniscient, omnipotent, and infinite beings? If He is all those things, then He could easily grant those things to all of us if He wanted to prove Himself. Of course, if He did that, He would no longer be a singular entity. We would all be gods, too. So, in a sense, the only way for God to prove Himself is to annihilate Himself – or to create an afterlife wherein we became infinite but not necessarily omnipotent.
This also reminds me of the Golden Compass books, which were interesting at least in part because God was neither infinite nor omnipotent. How they will translate the second and third books of that trilogy into film is beyond me.