What you are asking is, could the gravitational pull from a single black hole overwhelm the expansion of the universe and send it into collapse.

To do this, the mass inside the black hole would have to equal the mass outside of it in order for the gravitational field to be cosmologically important. If you have a black hole that has the mass of the universe, you already do not have a universe that is expanding. The material would be dragged into the black hole before it could get very far away, and this condition would have to have taken place when the universe was very young.

Now, according to physicists such as Stephen Hawking, it may be possible that matter flowing into a black hole could form a separate universe in another part of our spacetime, or even in another dimension. We have no way to know if this is possible, but in that case a black hole could form another 'Big Bang' in a separate universe. This is all speculation, and makes for good science fiction but not much else.

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