Hmm. "Subjective experience" doesn't feel the same to me as "imagination," but they're related I suppose. My experience of the world is real, as you would probably categorize yours. Invisible and unexplainable, not at all...see the many suggestions on this page. "Unprovable"; 1) if you've experienced it directly, your proof is there but it's limited to one person, 2) all mathematical systems break down when pushed to a limit (Godel's incompleteness theorem, the necessity of different physics/math under different conditions, etc.); we're talking about a way to encompass all of these things while adhering to a concise definition, it's hard.

I actually think these academic discussions of "what is god precisely" and "how does it work" only really sway a small subset of people. IMO it's "try these techniques out for yourself and decide for yourself," not "surely this explanation of the entirety of existence will sway you!" I'm with you, I don't think there's a formal text definition of god that ever would have convinced me to "believe." Either you have a notion of a higher power or unitive/connective force and have experienced it, or you haven't and you're working with the evidence you've got (math, the Bible, whatever). Take a few psychedelics or do a bunch of meditation and you'll end up feeling like most practitioners do, which is that you have a strong ineffable experience that doesn't translate well into words. Or don't! God's just a made-up word anyway for an aspect of the universe / human experience that we have a hard time defining (one of my definitions).