Baluncore, I just got back. You know the condition of criticality for the Schw. BH. If you get a certain concentration of mass within a certain radius in a non-expanding space then it will form a BH. Or if the rate of expansion is so slow it can be neglected.
But that does not mean that the same concentration of mass would always form a BH in a different context---these are two different solutions of the GR equation, the math would not necessarily work.
An extremely rapidly expanding space (high Hubble rate H) can TAKE a lot higher density of mass without collapsing.
I don't want to go into anything technical just give an intuitive assurance that it is OK. The very early high density rapid expansion phase does not actually spell BH. Other people, if you ask further, can give details. Or if it turns out to be easy to understand from what you find by doing a search, so much the better.
Oh, both the BB and the BH solutions have SINGULARITIES which are failure points where the classic 1915 GR blows up and stops being reliable. So that is just a symptom that the man-made theory is incomplete and fails at very high density, so the theory needs improvement. People are working on improved (possibly quantum) versions of GR that do NOT have singularities ether at start of BB expansion or at the center of the BH. In some of these proposed improved "non-singular" versions there are quantum effects appearing at extreme density that make gravity momentarily repellent and cause the collapse to rebound, triggering rapid expansion "out the back door" causing a new region of spacetime to occur, not intersecting with ours. So there actually (according to some quantum variants of GR) could be a bounce in the pit of a BH, spreading out into a "somewhere else" non-intersecting region of spacetime.
In fact, Jorge Pullin is giving a talk about that this week at the big GR20 conference