Why would you accept the concept of other universes, causeless effects, or infinite regression but deny the supernatural?
The supernatural is an indistinct idea for which there is no need. All it means is "not nature" with no clear idea of what we are talking about. If we propose the supernatural, how about including the juxtanatural, inferonatural, exonatural, transnatural, protonatural, holonatural, and paranatural? Why not?
My answer would be because these words are not associated with any distinct idea of they refer to, there is n reason to posit them since they add nothing to our understanding, have no evidentiary support, and would be the solution to no known problem, which is exactly the criticism of the concept of the supernatural..
Even if a god exists and created this universe, that god is as natural as its creation.
The concept of the supernatural is basically used by theists to explain why gods are undetectable, to put all discussion of them off limits to science, and to support special pleading arguments that allow the apologist to insist on various criteria for the existence of the universe while excusing gods of any such requirement.
In contrast to that, other universes, uncaused existence, and infinite time into the past, whether they are correct ideas or not, are clear and distinct concepts that all share the virtue of being potential explanations for as yet unexplained phenomena. For example, the fact that there is something rather than nothing suggests to us that our universe or its source if it has one has either always existed or came into being from nothingness uncaused. One of those two ideas may be correct.
Multiple universes is a possible solution to the fine tuning problem, if in fact that really is a problem. If a multiverse is generating multiple universes of every possible "tuning," then this universe would be expected, and probably duplicated countless times along with others that might not be so hospitable to stable matter, life, and consciousness.
The multiverse hypothesis' only competition as an explanation for the apparent fine tuning of the universe is a god hypothesis, which is a flawed answer to the problem. What would a god need with physical constants, physical forces, and laws of nature? Those are the requirements of an universe running unsupervised and unruled. An omnipotent god just wills planets to move in their orbits. No gravity needed, no law of universal gravitation needed, and no gravitational constant needed.
A godless universe, however, needs physical laws and constants.