One solution to the black hole singularity problem is Fuzzballs, a string-theoretic proposal suggesting that what we thought was a singularity is actually a tangled mess of strings and branes, replacing the notion of a smooth event horizon with a quantum "fuzz" that preserves information. If true, this would resolve the information paradox without requiring firewalls or breaking semi-classical gravity near the horizon. Still controversial, but it’s one of the few proposals with a concrete realization in a quantum gravity framework.
My non-canonical and possibly wrong view of black hole singularities is that they can form in finite time (sort of) only in their own frame of reference but in any other frame they require infinite time so from our point of view no singularity ever formed and ever will from. And in practice, in this infinite time something might disrupt their collapse, like getting hit with similarly massive amount of anti-matter an turning into photons which might destabilize the whole process and let them get out in massively energetic event similar to Big Bang. Which I believe was the case with ours, so no white-hole singularity either.
This view is dismissed by physicist because in GR there's no way to unambiguously define simultaneity so they don't event attempt to consider what's "before" and what's "after" regarding remote events in strong gravitational fields so saying that singularity forming is "after" everything else that ever happens in the universe is a hard sell.