Religion

If we look at finite gods, like the ancient european ones, then we have claims that can be adressed in experiments, that can be witnessed and proven or disproven.
"Does Thor actually fly through the air on a chariot pulled by two goats?"
That question can be answered by a simple observation.

The problem with the biblical God is however that he is defined as infinitely this and infinitely that. Whatever information we can get about him through observation is tainted by the fact that we can never be sure whether we have seen objective truth or whether God has presented us with a subjective version of himself he wanted us to see.

Plus, looking at this from the mathematical side, it's impossible to gain an infinite amount of information from a finite experiment. We would have to observe God with infinite accuracy for an infinite time if we want to know whether he really is infinitely wise and infinitely strong.