How do you define proof? Current secular science decided long time ago that any data that has the potential to take us beyond what we see will be ignored on the basis that the reality can only be defined as something that can only be observed through senses. God is beyond what we see.
If God is another name for "reality" or "existence", then it is precisely the one thing that is most obvious and clear. In this case, it is impossible to know anything else without assuming God exists.
If God, as in the traditional defition, is omniscient and omnipotent, that means that he has the power to modify the reality constantly in a way that no proof of his [non-]existence can ever exist. Therefore, leaving a constant mystery.