That’s a very interesting question, I should say… And incidentally, science-fiction authors and astrophysicists have been thinking about the link between the Big Bang and black holes for years.
Thing is, you have to understand the actual nature of a physical force, such as gravity or electromagnetic force. Electromagnetic force is “carried”, if you will, by photons. That is, if two electrons pass side by side and repulse each other, they exchange photons to divert their course.
We know little about the actual carrier of gravity, but in theory it exists, and is called the graviton. Some nuts are trying to say it’s something esoterical called the Higg’s boson, but let’s not dwelve there. Even my Physics graduate head aches from the debate.
Anyway, we know absolutely nothing of “Time Zero”, that is; we have no idea what state the Universe was in “before” it exploded. I put “before” in quotes because there might not even be such a thing as a “before” to the Big Bang. Headache #2.
What we do know of the Big Bang is, the primordial forces of the Universe took shape after the Big Bang; in the few nanoseconds following the birth of the Universe. As the Universe expanded and “cooled”, all the physical forces began manifesting as distinct physical laws, and the carriers of these forces began manifesting.
So, a few iotas of time after the birth of the Universe, gravity began exerting a pull. Unfortunately, as everything was expanding at the speed of light, it was too late. Also is the fact that, for large masses gravity is important, but at that point, the Universe was barely the size of an atom, so other forces, such as electromagnetic repulsion, were at work. It took a good while before gravity stopped being the unloved child of the primordial Universe.
That’s not to say it didn’t do its bit of work back then; in theory, there may exist “micro-black holes”, subatomic black holes still roaming the Universe to this day, punching holes through planets and coming out the other side fatter. The idea is that, in the early Universe, there could have been high-speed collisions between elements that collapsed matter into subatomic black holes.
On the relationship between black holes and the Big Bang: I suggest you read Isaac Azimov’s ‘Black Holes’, which is scientific vulgarisation of the explanation of how black holes form. In the last chapters, he launches into a rêverie whereas he hypothecises that black holes may be little cosmic seeds called Cosmic Eggs, leading to other Big Bangs. Quite fascinating, if a bit out there.