If we assume that god, by definition, must be omniscient

Why must that be true by definition? Many of the Greek gods were clearly not omniscient, because the stories about them all involve intrigues and hiding things from each-other.

Also, you can’t disprove a god’s existence by making a logic puzzle that’s hard for you to puzzle out. Just because it’s a toughie for you doesn’t mean that it disproves the existence of gods.

That isn’t even a particularly difficult logic puzzle.