But that's the whole point.As I said, rather than write - 'doesn't believe God does not exist'', just edit out the double negative and write it as 'believes God exists'. That will save you a lot of confusion.
The belief "God exists" points at god being true. The belief "God does not exist" points at god being false.
And then there is the position that we refrain from pointing. We refrain from asserting the uncertainty of either position, because asserting uncertainty either way does us no good.