And since nothing can escape a black hole, not even light, how
did the universe grow bigger than this? And since the laws of physics
break down inside a black hole, how has the behaviour of the universe
been extrapolated back to earlier, denser states?
You're right that nothing can escape a black hole, but this did not affect the growth of the universe. Your question suggests that you are assuming there was a lot of matter packed into a small space during some point in the universe's history. This isn't the case - when the Big Bang occurred, there was a lot of energy released, but matter condensed out of some of this energy. The laws of physics were different at this early time than they are today - or rather, at the energies that existed in the young universe, the laws of physics acted in ways that are difficult to observe today.
It is generally accepted that following the Big Bang, the universe experienced Inflation. This was caused by the energies unleashed by the BB being repulsive, like magnets. Inflation was a rapid growth in the size of space, expanding much faster than the speed of light (speed of light is the speed limit within space, it doesn't apply to speed space itself can expand at).
The expansion rate of space was much greater than the
rate a black hole could have formed at, for instance. So, any bits of
matter that were close enough and dense enough to start to form a black
hole suddenly found themselves spread across a much wider distance -
they were no longer dense enough to form a black hole. Any black hole that had started to form would have been ripped apart by the expansion rate of space.
Consequently, the breakdown of physical laws within a black hole didn't need to be considered when extrapolating the earlier states of the universe.