People who claim the god of the Bible exists (or does not exist) are linguistically confused. The verb to exist means to have the potential to have its properties observed. My teddy bear exists because it has the potential to have its properties observed. It is meaningless to speak of "spirit of teddy bear" which has no properties of teddy. Things cannot be said to exist in the absence of their properties.
Yet, the common definition of god is an entity whose properties can never be observed. So, to say that god exists is to claim that the entity whose properties can never be observed has the potential to have its properties observed, which is clearly self-contradictory. Notice that inserting a "not" in front of this proposition doesn't make it any more sensible.
Now, if one's god does have properties that can be observed, then presumably one's god theory is falsifiable. For, to be observable, the properties of god must be distinguishable from the properties of things which are not god. If god is more than just a conjunction of observations, then it is a scientific theory about a sequence of observations, and therefore, it has to be falsifiable. Of course, no one I know believes in a falsifiable god.