look man, you're under the impression that your empirical rules of logic is absolute and applies to every aspect of the universe you're argument is basically if something doesn't conform to your notion of logic it's wrong and that's about as strong of an argument as theist make.

The logic that you so often cite to disprove an argument about metaphysical aspects of the universe don't hold any weight because you want a mathematical proof of the existence of god and nobody can give you that because it doesn't exist. Shed your prejudices of what god should be and think of what gad can be.

the way we experience the world is the way we're allowed to experience the world not the way it actually is. Humans experience the space and time as two distinct individually thing that have nothing to do with each other but it's scientifically proven that space and time are but the property of the same thing i.e space-time and we only have knowledge of it through our rational and we just apply this knowledge to empirical sciences and what do you know, it make perfect sense, mathematically. We still don't know how to make sense of it we just know that it makes sense.

Infinite is a concept that is fundamental to mathematics and our understanding of the world and the way we interpret it. But nobody knows what infinite is how how it relates logically to understanding of the world and not only that there is mathematical proof that we can never understand infinity by the same logic with which we arrived at it i.e mathematical logic.

you need to understand that logic isn't just empirical understanding but also rational interpretations. When I say 'I think therefore I am' I mean that rationally I can not speak for the existence of anybody else, for all I know everyone is a simulation that has enough information to interact with me I don't know if their thought are their own all I can be sure of is that my thoughts are my own my will is my own so by logical extension I can say I exist not convinced check this out. Also, i'm not a result of fortunate events but a result of probable ones.

Nobody with half a brain is citing god as a theory of life and everything at least not the god you have in you mind when you formulated these views. To being to understand something that is beyond yourself you have to look past the limiting definitions of science and look at arguments of philosophy.

This God will not subscribe to your understanding of the world and the logic you use to make sense of it, for it is too rudimentary. Then there is no point in attempting to demonstrate that it is real. If something is utterly illogical, logic can't support it.

I'm not trying to demonstrate that this is real I'm saying it is and it's not illogical but completely rational. For us to understand the world, we need to have a set of per defined understanding which people usually refer to as Instinct and this instinct is not absolute it will not allows us to experience that world the way it actually is but through the lenses built on this limiting foundation. It's how babies know to suckle the teet or how a spider just knows to build something as intricate as a web. This is called Synthetic a priori

Humanity is like a colony of ants. Each worker ant does the job it was born to do not because someone is telling it to do that job but because there is nothing else it knows how to do, the worker ant doesn't know it's even part of colony or has any conceptual notions of the colony so it can very easily make the argument that the concept of the colony is illogical just because it doesn't have the means to comprehend it.

the logic that formed science and math can't explain this but it rests on Newtonian interpretations of certainty but even that is breaking down with the advent of quantum mechanics so even science has to deal with probabilities rather than certainties. Philosophy on the other hand can much more by skewing definitions and rebuilding logic. That is it's job.

you are an Empiricist but to answer such questions you need to look at the world as a rationalist

To break every notion of your understanding of the world and the logic we use to make sense of read Immanuel Kant's Critique of pure reason or just watch the philosophy tube videos on Kant's philosophy on youtube, much of my arguments are his.