I agree that one option is it came about from itself an option you really didn't eliminate except to assert it can't be true and the universe requires an external source. I don't think thats a given. In fact, god ends up with he same issue just pushed back a step prior to big bang. Then again god exists as virtue of itself or external and conveniently you stop the necessity of external source there. That is rather convenient but unnecessary.
I am not qualified to assert truths about existence myself. I get them from philosophers and cosmologists. It has been the dominant opinion of those most qualified to know that nothing will never produce anything. There are mantras that state this that are 3000 years old.
God most certainly does not have the same problem. The two ways this argument is stated are:
1. Anything that begins to exist must have a cause.
God did not begin to exist. BTW this one has been called the worst argument against God in the history of western thought.
2. That things must have an explanation for their existence within themselves or externally. God requires no external explanation, he contains his own explanation for existence.
In neither case are God and the natural in the same boat.
God as a concept must exist as an aspect of it's own nature. That is among the definitions of God. Does not make him true but does make him in no need of an external cause or explanation. The universe does not contain it's own explanation or cause. I can't list all the reasons why but I can supply the denial (as an impossibility) of the most popular counter claims by one of the most immanent cosmologists on Earth if you wish.
If universe needs something external why is it that god would still need to create from nothing. If god creates using himself then may as well call it all at once, god became at the same time as existence, a cause unto itself without having to bring in nothingness.
God is eternal as a concept and by revelation. There is no reasonable claim to a 15 billion year old God anywhere. The universe is widely believed to be about 15 billion years old. An eternal God did not create the universe when he began to exist because he did not begin to exist. He was described with the exact characteristics modern philosophy says must be true of whatever caused the universe by men who lived 3000 years before they were known. One of those is personal agency, which means the ability to chose to act. The universe is not a necessary creation. It could have not existed. God chose to create it. That means there was a point when God existed but it did not. BTW that would have to be true of any cause of the universe.