How is it possible to categorically claim that God does not exist.
You need to be asking "How is information possible? How is expression and interpretation of information possible." The answer to these questions illuminate the truth of what and how everything actually is.
The truth actually is known, describable, and provable, but requires understanding some things that are not easy to grasp for everyone.
First it helps to understand a fundamental limit of reality. Exact duplication of information is an impossibility, everything is variation otherwise there's no coherence to distinguish definable identity. If an essence were to be an exact duplicate of itself it would just be the original essence leaving no difference for variation, hence no relative change and no synthesis of information.
Next we quickly define "nothing", (which it's okay to not "believe" in) we understand any true origin of something must be understood as being of beyond the horizon of being something, hence the term nothing. Nothing agreeably isn't anything at all, though that's an understatement, to maintain this identity of having no identity is still to maintain an identity. This is a recursive self-reference paradox.
Remember those things, and now we move to the good stuff...
Trifold synthesis is the foundation for what makes interpreting and expressing information possible.
A good analogy to understand this (and appropriate for this topic) is the religious trinities. In Christianity god is constructed of three elements but not divisible by them. The father, the son, the holy ghost. These are all 3 very separate things, but together god is expressed. In Hinduism this same concept is described as Trimurati. Here we have Brahma being constructed of Brahma, Shiva, and Vishnu, but all are Brahma. These gods are personifications of creation, destruction, and maintenance. So this 'bits of three to make one' concept is the main point of this analogy. Means nothing right now, I'm just trying to begin the illustration.
The second analogy which is more immediately related is injective function. It's a logical concept that describes a way to preserve identity. It requires 3 elements, (x) = x ≠ y. Or this can be described in words, we say a functions' domain can never be mapped to it's codomain. There's 3 elements required here (1. function, 2. functions' domain, 3. functions' codomain) To preserve identity of functioning or coherent information there must be something comparably unique to allow for any identification to be possible.
So in the hypothetical case you are left with nothingness, have no fear because it's impossible. This paradox of nothingness actually manifests a trifold synthesis of information. Inflation then occurs from the recursive inverse deduction of an absolute identity (specifically absolute nothingness). And we can prove that nothingness is real.
Since you are an occurrence, a set of information, an existence of some sort, absolute absence is irrational as there's at least been you to compare to. However since there's always at least the essence of your occurrence to compare to, an absolute absence of absolute absence is actually rational, and not just a linguistic mishap, rather an intensional paradox of nature.
This is how you get everything from nothing. To understand beyond that, to visualize the evolution of space, and eventually our cognitive minds from this intangible information you have to study quaternions and monads, and read up on Kant, Dirac, Schrodinger, Hamilton, Hofstadter, Hegel. You need to understand the principles behind holography and the wave structure of matter. Then with all that understanding just look at the world, the cosmos, the microcosmos, the nature, and you'll see the true origin of fractally recursive self-reference resonant in all things even in our behaviors and cultures, etc...
Only a handful of people probably grasp this, and even the ones that know this don't quite know they know. Its hard to accept nothing is actual when it actually isn't. It's difficult to think backwards and invertedly about the same thing. It sounds insane to some because it's like redundant nonsense, nonetheless its why you get infinity when you divide by zero. Its why we have any self-reference paradox or any measurement problem.
If you want to read a recent philosophical paper that does a fantastic job of describing the quantum computing aspect of monads in relation to a theory of everything, look up Darius Malys. Or if you want a mathematical point of view from wave structure theorists about quaternions look up Geoff Hasslhurst or Milo Wolff. Or for cool wave physics graphics look up Gabriel LaFreniere. If you want me to explain more or something, ask
Here's some clarifications that might help answer some immediate questioning.
absolute absence is irrational yes. this is a paradox in its own and that is why it is irrational. its difficult to grasp I know, but an absolute absence of absolute absence is whats provable, by the fact that anything exists at all. It doesn't matter if you think you existed before or not, just the fact that you have ever existed negates absolute absence. We're speaking of absolutes not just conceptual absence during a single moment but of all moments.
yes man made math, but math also made man. Likewise the universe made man, and the universe made math, and man made the universe. This is all literal. The problem is you're thinking of things as being separate, but they are interconnected as only one system of the totality of everything, which also isn't actually anything on the surface. All the essences are inside this nothingness (or unattainable absoluteness).
See man made math, from observing consistencies in nature (the universe)
Math also made man, see most immediately you were conceived through human reproduction. This is a very complex mechanism involving molecular chemistry which is driven by quantum mechanics, which is driven by the very mathematical logic of monads and quaternions I refer to. Of course this doesn't clearly describe anything in detail because there's so much involved in all of these fields but you get the point. Maybe the biggest concern is how does the mind arise in man to be able to create the math? Well it's all more of the same recursive self-referencing that is the logic behind preserving identity to begin with, only filtered through countless systems of the same fundamental concept of trifold synthesis.
likewise man made the universe. Only self-aware entities will be self-aware. coherence of self or world is only available for the self-aware and coherent. This is why everything seems so perfect for life. The planets in the right place the temperatures right, all the right things happened just perfectly, any different and we wouldn't be here. Exactly, that's why we are here. We would only be where we could be.
and yes in the real world if you divide by zero you have what you started with, which is everything (potential infinity). Your mind develops categories, but they are subjective to only your mind. Categories are analogous to categories of other minds. This is the same for all things. The most fundamental form of this being all monads in relation to all monads. In your mind you can perceive dividing something you can experience the interpretation of it splitting into multiple unique new pieces derived from its former whole self. But in reality its just a bunch of waves splashing around, waves of space driven by quaternions. You could never divide something into a smallest piece (or number) because there's also not actually anything there, it (space) is just in our minds. I know that last part probably sounds the most insane. but that's the complexity of the world, and the truth is the truth, though it may take time to wrap any large populations heads around understanding.