I don't know what you mean by "supernatural," but the kind of naturalism I explore is pantheistic and cosmicist. Scientists have effectively re-enchanted nature with quantum mechanics, black holes, and the like. That's not to say petty miracles are possible, the kind that parochial, self-absorbed creatures pray for; rather, it's to say that every speck in the universe is strange in view of the universe's self-directedness or godlessness.
So if you're talking about the very early stage of the universe's self-unfolding, you're already practically into the supernatural even on atheistic grounds. Life as we know it wouldn't have been at home in that early stage because molecules wouldn't even have formed. The question of "where" the first speck of stuff or singularity came from is the same as asking why one stage of the universe's evolution proceeds to the next without any intelligent direction. This is Hume's problem of induction. Of course, we posit natural laws to explain the transitions, but we're not rationally entitled to say the stages are necessarily connected.
But to answer more directly, I'd say I certainly don't know where the singularity came from or why it was as it was. In "Atheism and the Endlessness of Explanation," I argue that naturalistic explanations are antithetical to ultimate, final ones, because naturalists explain X by positing Y, which obliges them to explain Y by positing Z, and on and on it goes.
And I'd say that the theist is in no better position by positing God because we can just as easily ask where God came from and why he's one way rather than another. So the real problem here is that curious, insolent mammals like us may not be satisfied with any ultimate explanation.
Natural selection and other such mechanisms explain how the eye evolved. Genetic variation, environmental pressures, and enough trial and error over a long period of time, and organic processes are sculpted to generate the illusion of intelligent design, of the organism's fitness to its environment.
Even if Darwin's explanation isn't perfect, even if the evolutionary biologist's understanding of life is limited, the naturalist is in a far better position than the theist who says that the whole thing is just a miracle. The theist offers an anti-explanation, which is necessarily inferior to any genuine, reductive explanation, even to an incomplete one like natural selection.
If you're asking whether I'm satisfied by natural selection as an explanation, as I say, I view all naturalistic explanations as inherently strange and thus philosophically or existentially unsatisfying. We want an ultimate, absolutely final "explanation," but that's a contradiction in terms. Genuine explanations are incomplete and reductive; they reduce X to Y, which means they explain one thing by positing something else. This mode of explanation is instrumentalist, Promethean, and Faustian, as I put it elsewhere. These explanations enable us to dominate our environment (perhaps self-destructively).
So what you're really asking is whether naturalism is more satisfying that theistic supernaturalism. The fallacy there is in supposing that the facts have to answer to our preferences. That runs against cosmicism. Just because one worldview may be more comforting than another, doesn't mean the comforting one is more likely to be true. We think too much of ourselves if we presume otherwise.