you can't prove the nonexistence of anything-
Not exactly true.
If the exhaustive method can be employed ( one of many scientific methods )
the a nonexistence claim can be proven.
If one claims that a toilet does not exist in a certain room
and the room can be exhaustively searched,
then that claim can be proven one way or the other.
Regardless of what Atheists say, the "nonexistence of God" can NOT be proven (science shows that),
That's why the burden of proof is on someone trying to claim the existence
The burden of proof is on the one making a claim regardless of whether
the claim concerns the existence of something
or if the claim concerns the nonexistence of something.
One who claims "the belief in the nonexistence of God and that the belief does not rely upon faith"
bears the burden of proof to show that either a) God does not exist or b) that they do not rely upon faith for that belief.
All atheists rely upon "faith" and that can be proven (and just was proven :-0) ).