Which came first, the Quantum Singularity or the Supernova?

While a supernova can produce a black hole, which contains a singularity, a quantum singularity is merely a hypothesis at best. See this for an discussion about a quantum singularity.

From your link, ”... In fact, since singularities are infinitely small according to relativity, they are expected to be quantum mechanical by their nature; a theory of quantum gravity would be required to describe this behavior, and no such theory has yet been completed.[1] On the other hand, only one kind of singularity has ever been observed (black holes)...”
Ergo we shall continue for the purposes of this discussion to consider the Quantum Singularity in the original question to be a Black Hole.

@Dan_Lyons I don’t know of any theories about black holes other than collapsing super novas creating them (I’m sure that if there are, some Flutherite will tell us about them). I had asked a question some time ago on Fluther if a singularity could be smaller than a one Planck length diameter and still exist in the physical universe. Since the mathematical definition is that a singularity has no dimensions, having no “space” for mass to exist, yet having an immense gravitational force, seems improbable.

It does seem improbable @Bill1939 , and yet when you understand that a black hole is a supernova which has collapsed upon itself, it begins to seem more and more probable.

@Dan_Lyons my conjecture is that a supernova collapses into a Planck singularity, a sphere with a diameter of one Planck length or greater. However, I realize that this notion could be false.