That sounds suspiciously like "they were inside a region with enough mass to form an event horizon, but they escaped because they had enough momentum", which in turn sounds like "we can escape from inside an event horizon if we just move fast enough". Can you explain how that's not what you're saying?
I wish I had a straightforward answer to that. I'm sure the answer is some combination of cosmic inflation and dark energy, but by all means it appears the early universe either narrowly escaped, or simply is a black hole, that singularities are a flawed concept, that nothing is escaping the universe, and we are all stuck moving forward in time, and that the infinite future is the singularity.
I don't have an answer either. But in my amateur opinion, of the available options, I lean toward "is a black hole". If all the mass we can see adds up to a black hole the size of what we can seen, then if you add all the stuff outside the light cone, it should add up to enough mass to make a black hole radius that includes the distance out to there.
But that leaves us with black holes forming inside a black hole, which I have absolutely no idea what to do with.