Black holes pull anything and everything that enters past the event horizon into the singularity. What if the current unknown output where all of this infinitely condensed matter goes to is the creation of new universes through 'Big Bang' events? What if that matter eventually once again expands outward after the compression caused by the black hole no longer has such a great effect on matter in the singularity, possibly caused by an eventual large span of distance? Could this be the beginnings of additional universes, i.e. new 'Big Bangs?' Could our universe be tied to a black hole (or multiple black holes) whose output from its originating universe is the matter we have around us in our own universe? How large would a black hole have to be in order to collect enough matter for additional universes that they feed to have enough mass to grow, particularly to our own universe's current and expanding size?
Black holes pull anything and everything that enters past the event horizon into the singularity
unknown output where all of this infinitely condensed matter goes
Here's your problem.
You probably read some terrible explanation about how black holes crush everything down into the singularity, this point of infinite... whatever.
That's a crap explanation. The singularity is, literally, a mathematical solution inherent to the equations governing gravity. Generally GR operates on smooth surfaces, the "manifolds", but several mathematicians demonstrated that in a black hole the smoothness leads to lines that just end. Not so smooth...
But that tells us pretty much exactly zero about "what's inside". It certainly doesn't specify anything like "infinitely condensed matter", although perhaps there are other reasons to suspect that. There's another thread on this from today or yesterday you might want to hunt around for, I can't find it now.
creation of new universes through 'Big Bang' events
As far as the math goes, no. This is for the same reasons that you can say for sure the universe is not just a big black hole.
"Being a universe", at least the ones we can think of, has some specific requirements. Those are not met at a singularity, AFAIK. But more broadly, the logic here is "well A is weird, and B is weird, so are A and B the same thing?". Generally the answer will be "no".