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.