You raise an excellent point---the problem of a purely materialistic and deterministic universe.
With regards to the fact of my thought processes being affected by my material composition and brain structure, your statement reveals the inherent contradiction of pure physicalism.
In a purely material world, my thoughts are not really my thoughts as much as they are chemical reactions caused by other chemical reactions. Thus, my beliefs aren't really the product of my assent to a proposition, but the physical effects of material interactions.
If such is true, then "you" (for whatever "you" can be understood to be in such a paradigm) do not really believe or disbelieve anything. Your lack of belief in a Deity is not the product of any "rational" thinking (for what can be rational about chemical reactions? Or what truth-value is created by a neuron firing?) or being more open-minded, or for anything other than pure random chance from arbitrary causes.
If the universe is purely material, and things such as beliefs are meaningless, then science and naturalistic philosophy are also impossible positions to assent to. If purely materialistic Neo-Darwinian Evolution created our minds by pure random chance, then it follows that our rationality is also arbitrary and not connected to reality. Thus, one cannot "believe" in the evidence of naturalism, much less "rationally" believe anything.
Materialism undercuts its own epistemology.
I didn't meant to attack it from a purely materialistic point of view. I was merely point out that the mind is inexplicably linked to the brain. Without a healthy brain, one cannot have what we consider a healthy mind.
As for materialism, especially very strict materialism, we don't know much about physical reality, much less about the brain to have a truly meaningful discussion outside of a sketch framework/argument. Too many of the puzzle pieces would be misses.
As I responded to Slice earlier, I don't subscribe to a lot of the seeming "randomness" as being truly random. Hell, 200 years ago, people getting sick seemed awfully random and superstitious. Now, we have germ theory which takes once thought "randomness" out of the equation.
In genetics, we are finding and understanding more about the mechanisms and structures of DNA and the process (including various proteins) which are taking once thought "randomness" into less random, highly probably event areas due to structure, etc.
Thus, "randomness" historically coincides with ignorance. However, that is not say that everything is or must be determined either.
Also, you state that there could be a universe where A & ~A exist simultaneously, but how? Because you just said there could be one? I'm sorry, but just the statement that such a place might exist is no different than stating that God could make a round square.
In fact, while we are on the topic of other universes, is it possible that there exists in one of these alogical/illogical worlds a God of some sort? In fact, why can't a God both exist and not-exist there, according to your paradigm?
The fact is that abandoning logic at the Big Bang is an unfounded rationalization to explain the gaping hole in materialistic philosophy's cosmogony. It is no different than the type of rationalizations that theists make about how "we just can't understand God."
And did our understanding of geometry change when we discovered/invented (depends on how you view things) with non-euclidean geometry? It could be done in ways we can't comprehend. If you put any stock into String Theory, M-Theory, etc., you would have extra dimensions where such may be possible.
Again, this conversation reminds me of this quote:
"Every man takes the limits of his own field of vision for the limits of the world." ~ Arthur Schopenhauer
You seem to be necessitating other existences based off your own.
As for the Gods/creator in other universes, it could be possible. Again, perspective. To an ant, we might seem like Gods. If we were to create a computer simulation (which is being attempted at this very moment) to create self-aware beings within the simulation, then the creators would seem like Gods.
Perspective and relation to other things are critical. It can change the whole equation.