I am starting by assuming neither premise is necessarily correct. And arguing
I then consider the laws of physics and nature, and see if it makes sense that it can exist without a super natural cause.
Since I know nothing little about super nature...I am uncertain initially as to if it could exist without an external cause.
However nature, without super nature does not seem to be able to. Everything in it, in whole or in part has a cause outside of itself. It makes no sense to allow that the whole thing together is an exception.
Let me expand on my reasoning for this last assertion:
We all would accept a hamburger can not simply come into existence by natural law with no external or internal cause (albeit a naturalist would also reject external causes as non existent). Simarily we would agree about any finite subset of nature as well. This we know as a very well established principle of nature.
So now, consider all of an eternal nature rather than a subset--which I think is the only part of this argument that is not immediately obvious--I say that logically, it would need an external cause as well:
Going back to infinity in time (or if you like in a cause and effect chain or web) just postpones and multiplies the inevitable need of an initial cause to an infinitely large balance. Every iteration just results in more stuff that needed to be caused by something external. Does one really have to be a competent mathematician to know what that limit adds up to? Mathematicians aren't asked to add up the limit of 1 over n as n approaches infinity. Philosophers need not bother to do the same. Every iteration back to earlier causes makes merely more stuff that can not exist without an external cause.
I am a very skeptical person, and great lover of reason. Which caused me to reject naturalism. I regret that not everything in the Heavens is something I understand. Nor even everything in nature. But that gives me no excuse to refuse to accept what I do understand about nature. Including that she can not be the whole picture.