You have answered your own question if you will only suppress your intelligence long enough to see it. God is by definition infinite. Proof would make Him finite, therefore destroying His existence as God. So, where do you go with that? A paradox or a reminder that there is something beyond our abilities?
If you want to ponder a little more, caution!, it may require unsuppressing your intelligence, ponder existence, not just of yourself and/or God, but as a definition.
See thinking can be fun far beyond this equals that, cause and effect.