Somehow we've transitioned from the Big Bang to black holes, but the same principles apply.
General relativity is a classical field theory that describes space and time through a gravitational field. Field theories propose that matter interacts with a field, such as a gravitational field or electric field, instead of interacting directly with other matter. General relativity is classical in the sense that it does not account for quantum mechanical effects; therefore, we might expect that general relativity does not apply (breaks down) in the realm of subatomic particles or minuscule time scales. The black hole singularity appears because we're applying general relativity in a realm where quantum mechanical effects are present. There is no physical evidence that supports the singularity and the current state of research involves building a theory of general relativity that includes quantum mechanical effects so that the theory does not produce a singularity.
we made that transition because you asked me to describe how they are applied practically
"There is no physical evidence that supports the singularity"
you are disagreeing with probably the most famous physicist alive in our era stephen hawking
"However, the expansion of the universe, is like the time reverse of the collapse of a star. I therefore want to show you, that observational evidence indicates the universe contains sufficient matter, that it is like the time reverse of a black hole, and so contains a singularity."
despite that... i agree with you, most of the discussion on this is speculative and distinguished people in the field appear to disagree on this a lot, which was my argument to begin with