Humans are finite.
God (*if* he exists) by nature is infinite.
If a human (finite) proved God (infinite) existed it would be on human (finite) terms because we are unable to conceive of the infinite.
Thus, the God that would be proven if humans did prove that a God existed would be a finite God because it would have been proven by humans who only have a finite understanding.
This wouldn't be God then, because by the very nature of God he is infinite.
Let me try to express this mathematically.
A = humans or finite
B = God
A only proves through A (Humans only prove by finite measure)
B is supposedly proven by A
Because A can only prove A, through the first premise, then B becomes A.
B = A
Thus the "God" that humans have proven is finite.
Thus, if anyone ever wanted to prove to me that God didn't exist all they would have to do is prove to me that he did. Then the God that would be proven would not be infinite, and thus not God. That God would not be God and God would not exist.