You highly understate that. "some" have indeed theorized about the big bang. But "some" in this case happens to be cosmologists and astrophysicists who have dedicated their life to discovering the nature of the universe. Einstein, and Lemaître, to Hubble and Bethe, scientists have worked on it for decades, using the work of those who also devoted their lives to the search for the nature of reality, and when the dust cleared the Big Bang model is what stood above the rest. If by "some" you mean the scientific community as a whole after decades of research and analysis", then I can accept its use. But I feel as if this is not the case.
Also, a great misunderstanding about the big bang is that people think that it state "nothing becomes everything". But if you asked any physicist if the Big Bang theory says anything of this sort, you would be quickly corrected. The more accepted view is that all of the mass in the universe was held in a singularity of matter. There was something and everything else came from that. Please never say what you said about the big bang again, because it is a false belief that holds no weight.
Also, the solution you posed actually gets us in no way shape or form closer to a real answer and is no way a shut down argument for the existence of your particular deity. I find it quite convenient that you state that your god fits the bill, but ignore the fact that the infinite number of other deities also fit that same bill. Also, there is absolutely nothing that causally connects said eternal deity to the creation of the universe (just because he/she was there, doesn't mean they had anything to do with it).
I also find it convenient that you go down claiming that something never comes from nothing, but make one exception for the eternal, had-no-creator, god that you believe in. If you are willing to make an exception to the rule there, why is it impossible to make an exception elsewhere. Why couldn't the matter and energy be eternal like you originally dismissed. What if the energy and matter are god? Have you ever considered that as a possibility?