The Mystery of the Infant Universe's Survival.

TL;DR
The early universe did not collapse into a black hole because the creation of a black hole relies on not only incredibly high densities but also density differences. The early universe was incredibly dense, but it was dense everywhere, with barely any differences. Additionally, the early universe was dynamic, evolving, changing, and most importantly, expanding. The rules of black hole formation simply don't apply in an expanding universe. There wasn't enough mass in the universe to counteract the natural expansion of the universe and force it to collapse.
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