I’m Western esotericism, names have power beyond simply being signifiers for the thing they represent- they embody some part of the thing they represent. The word “fire” contains some intrinsic “fire-ness” but not the whole picture. After all, everyone has different names for the same thing. It is thought that everything has a “true name” that perfectly encapsulates all things about it in their entirety, and this true name could be found by intense study, meditation, or etymology. The Bible pays a lot of attention to names in this way. Adam, the first man, names all the animals. Genesis pays a lot of attention to the names of places, and a lot of stories in Genesis are essentially folk etymologies of locations. God’s own name is of special importance, and its meaning was revealed to Moses by the Burning Bush. Even today Jews believe that even saying God’s name is powerful and dangerous and that only the High Priest would be allowed to say it once every year during Yom Kippur. Jewish folklore says that even this name is merely a part of God’s true name, and that Moses pronounced a longer more complete form of The Name to part the Red Sea, and some systems hold that there are even longer and even more complete forms that have been known to rabbis in the past.
There are definitions of “God” that I feel are hard to prove, but others that are easy. For example, of your definition is “God is the ultimate cause of the universe” then it’s pretty trivial that if everything has a cause there must be an end of the chain. Of course, this the could be a computer program running the universe simulation or even just the laws of physics themselves if those are truly causeless. But nonetheless, it’s still a somewhat satisfying definition of “God” so I’m comfortable saying I believe in God. Harder definitions include “God is an omnipotent being” (which most of God’s traditional attributes can be derived from) and “God is the being described in the Bible/Qu’ran/other religious text” which I feel like are unprovable.
A lot of religious apologists will make arguments in favor of the easier definition and then try to claim that this means their specific view of God is real. Personally I think that’s insane. Like “there must be some end of the chain of causality therefore God became a Jewish carpenter in the ancient Roman Empire.” Even if you’re Christian that should be a bad logical jump.