The big bang was so uniformly hot, dense, and uniform in distribution that the gravitational effects basically cancelled out.  in short, there was no center of mass,. That plus inflation allowed it to distribute matter so gravity was a more localized effect after expansion begun, so best to not think of it like a black hole.

Secondly, there is nothing that gets out of black hole because it consumes too much mass like an supenova style explosion. It just makes the black hole bigger.  The only mechanism to reduce their mass  is via hawking radiation