There's no god, the answer is something way way way bigger than our brains could ever hope to understand. There are infinite reasons why infinite universes exist, have existed, and will exist. Trying to look for a simple answer is human nature; there is no answer.
Logic is a predicate for truth. Truth takes the form of sound, rational statements (note: root word of 'rationale' is 'ratio'). Truth, as it is relevant to us, does not exist outside of these rational statements. Accordingly, truth should be modeled in terms of the mind as it relates to the rest of reality.
The best model one can theoretically come up with to explain something must meet a few criteria: It must 1) Be internally consistent, 2) Comprehensively and soundly explain all information it attempts to do so, and 3) Introduce the fewest number of assumptions, ideally zero. Falsification of the model can happen on two levels. At a lower level, the model can be rendered internally invalid if new information is introduced which should be explained by it, but isn't. At a higher level, the model can be rendered externally invalid if another model, which is broader in its scope, not only explains all information in the original model, but synthesizes this knowledge with other information unexplained by the original model (the result being a deeper understanding which predicates any topological understanding).
In the universe, we are aware of two great opposing things. One of them is the exact opposite of the thing that entropy produces. The other is entropy and the things that it produces.
We see entropy at work tearing down the things that are exactly opposite of what it produces. We don't see any cause that could have caused the opposite of what entropy produces to exist. There is nothing at all that we can see that could have built the great marvels of the universe that entropy is destroying.
Mankind is part of the universe. The mind of man may be the greatest thing of and in the universe. The mind of man is the only thing that we see that has abounding intelligence and reasoning abilities. It is the only thing that can produce highly advanced "things" of intelligent design.
Because mankind has been around for a long time, and because we don't see anything other than entropy working for at least as long as mankind has been around, mankind and his mind have been deteriorating due to entropy, just like everything else.
As we extrapolate back in time, we move toward a place and time when either there wasn't any entropy, or else entropy and the exact opposite of entropy (whatever it is) were completely balanced. What would the mind of mankind have been like back then?
Whatever it is that could design the intelligent mind of mankind way back before it had deteriorated due to the addition of entropy, is God. Whatever this God is, He/She/It is still God... by the dictionary definitions.
Ok, so you are proposing your own theoretical model. Let's look at it.
Responding in paragraphical order:
1) While it is true we become aware of entropy because we identify it as separate from its inverse, i.e. non-entropy, this dichotomy doesn't serve as a great basis for formulating a model of reality. Entropy itself is an abstract model of patterns which are directly observable in physical systems. This has deep implications for your model; I'll get to those as I go on.
2) Slight correction -- we observe that systems break down which both enables us to form an entropic model of closed systems, and also reinforces this model through continued observation. But yes, you are correct that we do not observe any direct cause of the processes we have modeled as entropy.
3) Although it's irrelevant, animals can make/build tools, homes/dens/nests, etc. which can be described as either extremely complex or extremely simple, based upon your perspective. But again, all of this is really irrelevant, anyway. The point is that we have no choice but to rationalize with logic and form the best theoretical models that we can, inasmuch as our human minds allow us to do so.
4) This is where the implications I mentioned in point #1 become important and relevant to your model. You cannot infer from entropy that the human mind is also moving towards disorder. This is because entropy, as I explained in #1, is an abstract (i.e. of mind) model of physical systems. Based on this information, you cannot conclude that the abstract mind necessarily deteriorates as it does not fall within the scope of the model.
5) Here, you start going all over the place. First, you're not going to get a fundamental understanding of anything through extrapolation. The process of extrapolating removes the ability to conclude at a 100% level of confidence.
Second, you make contradictory statements with regards to time. "Time" is better modeled in terms of "spacetime" where space and time are inseparable and synthesized in a unity of understanding, which thus provides broader scope than a discussion of "time" alone. Because of its physical components, "spacetime" can be modeled as a physical system, and thus one to which entropy applies. If you try to extrapolate back in time, you'll find that you can't assume any type of physical reality in which entropy didn't apply (and, therefore, can't assume any "time" at which entropy didn't apply).
Third, Einstein modeled via the Theory of Relativity that time is a relative function. The model itself could be described as a superpositional explanation of time as it relates to space. In contrast, you are describing/modeling time in a purely linear fashion. which falls short in scope to the Einsteinian model. The result is that a correct answer to your question, "What would the mind of mankind have been like back then?" would only provide a topological understanding of mind. Put simply, better models lending to more comprehensive conclusions must necessarily exist.
6) Here, your premise that something existed to create the human mind which "deteriorated due to the addition of entropy" is invalid for the aforementioned reasons (e.g. we can't conclude the human mind is necessarily subject to entropy based upon laws of thermodynamics, etc.).
What you
can say is something like, "There is some unknown cause, 'x', and for practicality I'm going to say x=God. And so, therefore, because the unknown cause exists, God exists."
What you
can't do is reach this conclusion that God exists, and then say that because God exists it embodies all the characteristics you think it does based upon your Biblical understanding of it, or any other preconceived notion of God that you might have. This precludes your ability to make any other statements about God, unless you can form a sound, theoretical model for it.
