You know, if we are talking about a simple definition of what a God is, the need fr an argument would not be necessary.
For instance, If you define God as "the entity/entities that created you" , then my Gods exist and observable. My (biological) parents created me. I could possibly include all my ancestors as well since they are necessary for my creation.
But, for some reason, there are theologians that wish to add more to their definition of God.
For instance, God is everlasting---I don't know of anything that fit this description except nothiingness. Is God therefore the Void? Empty Space? Can you give an example of something that is everlasting because the Universe or things it do not seem t fit the bill.
Another--God created the Universe. Here is what the op seem to try to prove. I like to take a quicker, yet a somewhat illogical approach.
Let us assume that what ever created the Universe is God. So it seems what is left to do is prove that the Universe had a beginning. And then claiming whatever initiated that beginning is therefore god.
Most people assume that Universe was created in/by the Big Bang. Let assume that and we are finished---The Big Bang is God!
However, praying to an event just does not sit right with most Theologians.
In the end, it does not seem like there are any of the Christian Theologians that like to use the Abrahamic definition. I mean, this is the basic premise they are proposing and wish to prove. And if there is proof of one of this God's characteristics, what proof do they offer for the other characteristics? Why would they try to argue that the God they proved to exist under one Characteristic is equal to the God they have described? That is a logical fallacy of Equivocation. You may have falsely described your god but were one of two characteristic of someone else God!
In short, trying to prove that the Universe was created/intiated/started is not enough!! you have a whole list of things to prove in order to demonstrate the Abrahamic God exists!! And I think some of it would be virtually impossible.
See. If they kept it simple, you would not have all these problems. You probably would not have atheists or agnostics as well because it would have been so obvious.....Like knowing you have parents!!
There are actually two things that are eternal. You are correct that nothingness is one of them. Notice I use nothingness in my first dichotomy for that very reason - because it is uncaused. The second is the other side of the dichotomy with nothingness, which must be eternal because it shares the dichotomy with an uncaused other side and the dichotomy must jointly exhaust all possibilities. If the other side of the dichotomy were caused, then it would not include the cause itself, and hence would not jointly exhaust all possibilities.
The other side of the dichotomy is all possible all inclusive states of existence, which is also eternal. However, as proven by the second dichotomy that only all possible all inclusive states of existence that can become real are real, then only all possible all inclusive states of existence that can become real are eternal.
But, because there is no inherent order to all possible all inclusive states of existence that can become real, the only real thing that is eternal is the constraint on those possible states having the ability to create them at will.
Hence, there are two - not one - things that are eternal, i.e. nothingness and the constraint aka God. And because these two are mutually exclusive, and because nothingness is not real, then God must be real.
I think I am missing something in your argument.
I am trying to find where the state of Real(I am not sure I am saying this right. Is it possible for something to come into and out of reality? ) is everlasting. I may have to reread your post again because I think I missed the proof for this claim.
Also, there is something else that is bothering me. Are you a non-theist? That is, you believe in a God but not in the theist sense such as theistic Gods have anthropomorphic qualities. Because it seems like that is what you are trying to prove: You idea of God is that God is the constraint of all the possible the states of reality. If so, you just need to define God as that and show that there are constraints
on possible states of reality. The Double Dichotomy argument is not needed.