The bible doesn’t prove god exists. The bible only proves that Christianity exists. There’s a big difference.
But you say “How can Christianity exist without a real, actual God?” As a Christian/Muslim/etc. you say your god is the one and only true god.
Therefore, logically, all the other religions must be based on non existent (false) gods.
That proves religions can exist and flourish without an actual god. And without proof that God exists, Christianity (etc.) falls into the same category as all the other religions that exist without a real, actual god.
In reality, god and religion are two completely separate concepts. The existence of numerous mutually exclusive monotheistic religions demonstrates that they are based on the perception of a god, rather than on an actual god.