There is only one way to prove the existence of something: by producing a TRUTH statement about it.
For god, one must first define what it is. Then all they have to do is produce 1 truth statement about it. If they can do that, then they have proven its existence.
To this day, nobody has been able to do this.
To prove that something doesn't exist, all one has to do is give 1 contradictory statement about it in the form of (P and not-P) at the same time, where P is a proposition. This is the only way to prove something doesn't exist, including a defined god. This is the PRIMARY reason why theists are hesitant to provide definitions for god.
Yahweh, Jesus, and Allah are proven to not exist using this rational method.
But a deist god, whom we know nothing about and can't be defined, cannot be proven to exist or not.