When the Big Bang created all the matter in the universe just after the Big Bang, why didn’t all the matter form a Black Hole?
Has it got something to do with the rate of expansion of the early universe?
Rock
Hi Rock
The big bang is an explosion of energy (universe), while black holes are created by collapsing matter (suns).
For a big bang to happen, the explosive energy necessary would have been far, far greater than any one piddly little sun collapsing in on itself.
Secondly, a sun only collapses when it has run out of fuel. By the time this happens, the expanding universe is well an truely on its way.
I assume you’re thinking of the point of singularity (where the universe begins) as the place for a black hole? If so, you’re not refering to a black hole (which is a collapsing star) but the opposite to the point of singularity. The answer would obviously mean the strongest force wins and if the one you’re proposing wins, no universe; if the other wins, bang! a universe.
The hard part to fathom is whatever happens behind the point of singularity is happening before time has existed, so as soon as the universe got sucked up again (if that were possible) it would never have happened. 
km2_33 is correct!
After Big Bang the expansion factor won over gravity, and it´s still happening with a tendence to increase! The reasons are somehow related with the dark energy/matter with appears to have the opposite efect of the matter we see. Once this dark energy/matter is, suposely, more then 90% of the total matter of the universe i guess thing turn easy to understand!
Look at Big Crunch theory for example. It will never happen because there is no enough “normal” matter to balance against the dark one. The consequence will be an accelerated expansion of the universe until all atoms are in is more basic form (where nothing more is possible to be created)!!!