The Universe was once a black hole?

According to the Big Bang theory the Universe has been expanding from a tiny size to its present size. The amount of m in the Universe has stayed the same (presumably) so at some point in the past the density of the Universe must have been such that the Universe was a black hole (it's size was less than its Schwarzschild radius). How did it manage to stop being a black hole and end up the size it is now?