A supernatural explanation would not be an explanation at all, by definition. Explanations imply cause and effect, ie a natural order. You are thinking of free will as some sort of supernatural phenomenon that evades cause and effect and therefore cannot be an explanation
I am not saying that anything can evade the cause and effect syndrome. I am just pointing out the possible error of assuming that all causes are limited to the deterministic chemical activity of matter within our universe. I am implying that human creativity can provide evidence for causes outside the observed deterministic behaviour of matter. Intelligent design does take place in our universe, as aptly demonstrated by human beings.
I think you are mixing up two rather different ideas here - creativity and design.
Most human creativity is really just cross-fertillisation of ideas from one media to another, such as when Darwin came up with his big idea, it was by applying thinking from a different discipline (economics) to the natural world; composers take inspiration from literature, and so forth. But further to that it is intriguing to consider that quantum effects are increasingly becoming understood to have some signature at the level of biological systems and so perhaps maybe human creativity owes in some part to some level of quantum indeterminacy.
Intelligent design, on the other hand, implies a deliberate, guided, fashioning of something, which is in stark contrast to what any quantum indeterminacy would give you, which is essentially a random, unpredictable quality, not at all what you want if you are trying to design something particular.