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.

Given the absolutes properties of god, its existence is probably one of the rare non-mathematical things which is possible to prove or disprove.

With actual knowledge, it's impossible to affirm that premise. Impossibility may change over time as it had with the capacity of humans to fly.

it is also impossible to prove that God does NOT exist!

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.