IMHO this conflates model with reality. GR is a model.
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.
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
[1] https://en.m.wikipedia.org/wiki/Fuzzball_(string_theory)