Or, maybe there wasn't anything until there was enough room for it to be in. Then you don't need a black hole.
Cosmologists like to toss about "expanding universe" and "inflation" as if they mean something, but they really are like gravity to Newton: a name for a process that can be described, but is otherwise wholly incomprehensible.
My understanding is:
1. there needs to be somewhere to escape to, for the schwarzschild radius to make sense, and there's no "outside" to the universe
2. we don't know how big the universe is or what it looks like; if it's infinite and uniform then there won't be any central point for a singularity
3. as others have mentioned, inflation is a get-out-of-black-hole card
4. the physics of the early universe aren't necessarily the same as physics now
It’s more that we had infinite density. Then space itself spread out.
Oversimplified disclaimer.