> there are exactly zero actual things with an infinite nature of any kind that I can think of

That's because your imagination is bounded by being a monkey that has spent its entire life in a finite environment — no offense. The universe, however, isn't bounded the limits of our imagination or intuition.

Yes, that's all very interesting (truly) but where does your actual lived experience come into play? That's the part I am talking about, the "in the universe" part, not the "could be" or "in imaginary parts of the possible universe" but the actual, experience-able universe. That's what separates math from physics and IMO math is the one that has to prove its worth not the other way around. I can construct endless internally consistent imaginary worlds with zero bearing on (any) reality.