Having assumed the initial expansion, however, the answers are what I already gave you: gravity (plus cooling, to put it simply); dark energy (or whatever you want to call it); and physical laws weren't different (the universe didn't 'travel' faster than light; rather, timespace was stretched and light stretched with it).
No, gravity is what prevented the Big Bang from happening any earlier...it was the force that originally bound all matter close together (remember that space itself exerts no force) per the inflation theory.
Nor did cooling happen. Cooling is a colloquialism. In reality, to cool an object you must move heat away from said object. This is why heat radiates away from a hot stove, i.e. the heat is moving away from said stove. Turn the stove off and eventually all excess heat will radiate away into the environment.
But the universe has no such place to move heat outside or away from it. Energy is neither lost nor made, after all.
So the universe didn't "cool" overall...all of the same heat was and is still in it (unless you can identify where it went). Note also that empty space can't hold heat (though heat could transit across it in some fashion).
And dark energy doesn't exist. We've never seen it in the wild or in the lab. It's a mathematical figment...a crutch...a tool of a mathematical model.