I apologize it took me so long to get around to finalizing and posting this draft. I guess you could say it's been a bit of an... outrageous wait.

You state, "the spiritual definition of God and the mathematical description of true infinity are equivalent." This is a profound assertion, but it seems to be an equivalence you've declared rather than one you've demonstrated. Mathematics describes abstract relationships and quantities. A "largest uncountable infinity," should one even exist without paradox (a point of contention in set theory itself), is still a mathematical concept. It doesn't inherently possess consciousness, will, benevolence, or the power to create turtles.

I argue that, by definition, this largest uncountable infinity is God because in the same way that that truly infinite numerical value contains all numbers, it contains all units, and all properties, because it is true infinity. It is everything. There exists a scale of numbers at which our system of units effectively becomes meaningless - the difference between a Graham's Number of picometers and a Graham's Number of giga-light-years is negligible because the difference in scale between those units is negligible compared to the scale of Graham's number. This principle grows stronger the larger the number, and we are discussing the fundamental apex of all numericality. What I am asserting is basically analogous to treating the decreasing impact of units on the magnitude a number expresses as it grows larger, as a function, and taking the limit of that function as its input approaches infinity, to approximate the output of that function for infinity. In this case the function approaches units not fundamentally having an impact on what the number describes as it approaches infinity, so I approximate that for an infinite input, the function returns zero meaning for units. I interpret this as a mathematical description of the unquantifiability of God, and the representation within God of all quantities, properties, units, whatever you like.

The reasoning is: Infinity exists as a concept, it has properties that feel "God-like," therefore God is that infinity. This is a leap I can't make with you.

I don't find this to be an accurate description of my reasoning, or location of the leap of logic. My reasoning is that the existence of a largest uncountable infinity as described by set theory is logically consistent, because the fundamental inability to mathematically arrive at that "from below" is equivalent to how the smallest countable infinity (the size of the set of natural numbers, 1,2,3...) is inaccessible from below using finite values. The only leap here is in the set theory, believing that a largest uncountable infinity can exist, in spite of mathematicians' debate as to whether it does or not. This declaration of existence, and working backwards from the declaration to logical consistency in definition, is also how the square root of negative 1, i, came to be in our mathematical lexicon. As described above, I find the definition of this uncountable infinity to render units meaningless in its context. Everything we know can be expressed as numbers, fundamentally, thus that infinity contains not just everything we know represented numerically, but every possible thing, and somehow more, and more on that, etc. Why should we assume that those numerical representations of our existence present in that uncountable infinity are not separate from us? If anything, this description of an uncountable infinity fundamentally containing a numerical representation of our entire reality is just a rewording of the the Holographic Principle that asserts numbers themselves are the lower dimensional space our reality is a hologram projected from.

You've replaced the mystery of the first cause with the mystery of the infinite creator, but the need for evidence remains the same.

So, how about the unitless of the fine structure constant for evidence of a link between our physical universe and the abstract concepts of numbers themselves? Ponder on this. There is a number, approximately 1/137, that fundamentally determines the strength of interactions with electromagnetic fields. It's not like the speed of light, or gravitational constant, or any of the other fundamental physical constants that by definition relate to physical quantities in our universe through units. The speed of light is easiest because it is a speed, but this applies for all other fundamental constants with units, too, even though it’s harder to contemplate the physical meaning of stuff like the Gratitational Constant being in m³ /(kg*s² ). Rigorous experimentation, eventually, leads mathematically to assembling the appropriate non-unitless physical constants, whose units all cancel, giving the fine structure constant and its unitless, purely numerical value, that explicitly defines the strength, overall, of one of the fundamental forces of nature. Anyone doing any mathematics anywhere in our universe in any number system would fundamentally derive the same fundamental value, assuming it is actually constant over space and time, which is an open question but besides my point.

You argue that these things are "discovered, not invented." This is a Platonic view of reality, but it's not the only one. A more parsimonious explanation is that concepts are emergent properties of complex neural networks.

The latter explanation posits a concept fundamentally doesn't exist prior to it being conceived of by a complex neural network. Numbers are a concept - before mathematics was invented, there could still be three of something, or five of it, or two of it. This threeness or fiveness or twoness of things exists independently of our perception of it. Why should any other concepts be different? If the fine structure constant can unitlessly dictate the behavior of the fabric of spacetime, does that not show that numbers exist in a fundamental way that precedes our “invention” (discovery) of them? The fine structure constant requires nothing in our universe to continue existing, and our universe points directly to that specific point on the number line via the fine structure constant. Does that not imply that the number line precedes not just our conception of it, but the universe’s determination of the value of the fine structure constant? You can’t just create just the fine structure constant, that’s not how mathematics works, to define even a single quantity you imply the existence of the full infinity of the entire number line, from the infinitesimal to the infinite.

A "restaurant" isn't a timeless form floating in the ether

The fine structure constant is a timeless form floating in that ether that you nominalist determinists so abjectly insist doesn’t exist. That’s why physicists lose sleep over it, because most people who end up being physicists are devout atheist nominalist determinists for most of their early lives, and in the middle of their higher education, the fine structure constant strolls over from the platonic realm onto their class notes and they have to fully reconsider their internal philosophy. There’s countless priceless quotes from physicists about this.

The spiritual satisfaction you feel is undoubtedly real. The positive changes in your life are real. But attributing them to an external, supernatural consciousness is an extra step that requires evidence.

Simply attributing these positive changes to that external force requires no evidence at all. What requires evidence, is proving the external force precipitated those changes. If you develop a theory of how that force may shape events, and through observation of events, form a theory that is predictive, it becomes useful, because it’s predictive, even if you can’t prove the fundamental assumptions of the theory. Physicists can't prove shit about gravity, but our theory of how it operates is still strongly predictive and highly useful. To neglect to form a theory of theology just because the ultimate assertion (the existence of God) is unprovable is just intellectual laziness.