Presumably, any concept that would hope to explain a "godless universe," is pointing toward the (infinitely) more likely alternative that, the God might Himself, came to exist, that way. That is, materialists contradict their own ideology, when they question "So, who created the God, then?"
In the rest of this document, I'm talking of merely stories, philosophies. I'm not necessarily guessing how the God truly might hae come to exist (nor would I care, because Islam does not hold us responsible to guess that). The point of story-making, is to demonstrate that, materialists, when they think further, serve only to justify Allah.
The evolution concept is certainly in that category.
I find that ironic that, in forums, most of the times, that is the evolutionists who ask that question ("For existing, if we need the God, then how did the God came to exist?"). Why would they not guess that with their ideology that, Allah might have just evolved?
None of the points we have to refute the species evolution, seem to oppose Him.
The concept of survival-of-the-fittest also might fit (with or without the evolution concept).
That fits the multiplicity of spontaneous entities, if there were. That is, if your materialism would suggest that somethings might happen spontaneously (explosions in vacuum), then Allah is explainable to have been that who fought and was the survivor. Then, not allowing new "upstarts" to come to exist after Himself.
The Quran is stating the "gods" issue. "If there were "gods", the Universe would not be so orderly." Thus, His stronghold style, is to fend off anarchy, too (if anything such as spontaneous entities might happen). That statement might have been His wisdom about personalities (knowing the law of being), as well as (possibly) having known the cases -- having faced, then killed/consumed the opponent spontaneous-entities.
No matter what "root-cosmology" we might think (evolution, spontaneous-first, survival-of-the-fittest, etc), we have to supplement that with the point that, Allah has consciousness. Now, active.
Allah is most likely creatively developing Himself. Thus, Allah is self-made.
Presumably, inferrable from what Abraham (a.s.) told about Nimrod's ugliness (suggesting that a/the god was supposed to be able to look good -- presumably by modifying oneself, if not by modifying the perception of the creatures, but furthermore, creativity might like to self-develop, therefore the self-optimizing option is fitting well.)
Humans might need gene-therapy, or surgical operators, to modify their bodies.
Humans learn mostly by acquisition. But with creatively tinkering, too. That fits Allah.
Allah is not mortal. Thus, His achievements remain with Him.
Allah is witness for Himself. Thus, that is in the general category of challenge-in-your-face. Do you have some evidence to oppose that? Whether rivals, or "beyond" ? Allah denies all such.
Do you suggest you know something He does not? No, unless you would lie. You only might try to philosophize baselessly, "what if?" In fact, way before that, you would not know how to resolve the question of "mind vs. body" about the universe we live in -- if that were left to philosophy, in defiance of all observables. Non-materialist, that is.
Besides, there is the Quran. That is, I had not started to achieve faith from such guesswork "meta-cosmology." Allah sent us that text, with Muhammed (s.a.s.) that now we have been informed muslims. We have nothing to oppose in that, nor any alternative story to support.