I assume that:
- most christians believe in a single one god (monotheism); and
- that this god is the christian god.
In that case, how do you know that the gods in other monotheistic religions do not exist?
How do you know that there are not multiple gods (polytheism)?
Depends on how you define the term "god", also as opposed to "God".
I believe there are many "gods", but there can only be one "God" in the Aristotelian sense.
I can believe Zeus, Mephistopheles, Screwtape, Amon-Ra, etc etc all exist. I must take their mythologies with a grain or 700 of salt, but nothing stops me from believing they exist. Quite the opposite. Where did they come from? Men's minds? Yeah, right. People aren't that stupid.
St. Augustine once proposed in "De Civitate Dei" that they were just immoral demons - citing the adulterous, murderous acts they asked pagans to do and to imitate. Tertullian lay similar charges against the pagan gods; if they are gods, why are men so able to manipulate them, or why do they depend on men to name them? Tertullian claimed not that they did not exist, but that they were demons. A loaded term in our time, but all it really implies is that they are spirits - however vile - who are not worthy of our worship.
I have no problem with the pagan gods. They pose neither me nor God Almighty any threat. They're little more than super-powerful man-like creatures.
As for other monotheistic religions, shortly, the Catholic Christian view of what God is is most liberal: God simply
is, or as Aquinas put it, He is the "essence of Being". All things "are", but only He possesses perfect "is-ness", if that makes sense. Anyone who understands God to be that believes in the same God as we do - even if we do not agree on everything He is. Usually the difference is a fixation on some point of God - like fixating on the fact that a cone has a circular face, to the exclusion of the cylindrico-triangular body that comes to a point above the circle.