Specifically, GR is a model that breaks down at singularities. That time "begins" at the Big Bang is a prediction of GR, but until we have a model of quantum gravity there's no telling whether that's actually true or whether the conditions at the big bang are something GR can't fully describe.
Similar to the singularities in black holes - everything up to a stone's throw of the event horizon is pretty well explained by GR, but as far as the horizon itself or the region beyond are concerned, there might be dragons as far as we know.
> That time "begins" at the Big Bang is a prediction of GR
I don’t think that’s right. If we interpret Big Bang theory as claiming that there is a singularity at a finite distance into the past history of every present event, then GR can’t predict what happened at or prior to that singularity. Whether time “began” then or whether there was “more time on the other side” is a question GR alone cannot answer, not a prediction of GR
Black hole singularities do not start right after their event horizon. The event horizon only demarcates where the black hole singularity becomes an inevitable (inescapable) point in all possible futures.
That's not what I was trying to imply, sorry. It's the singularity at the center where GR entirely breaks down, but there's also weird stuff going on below the event horizon (space becoming time-like and vice versa), that aren't present in, e.g. String Theory's Fuzzballs [1] (which, of course, bring their own set of thorough weirdness). So what I was trying to say was that while GR predicts some behavior below the event horizon, a full model of quantum gravity could predict something entirely different, and not only for the area just around the singularity itself but (maybe) up to the event horizon.
Similar to the singularities in black holes - everything up to a stone's throw of the event horizon is pretty well explained by GR, but as far as the horizon itself or the region beyond are concerned, there might be dragons as far as we know.