Why did the big bang not just produce a big black hole? Questions I've often wondered about:

If all the matter and energy were concentrated at a single point at the big bang, why wasn't that a black hole, or why didn't it form one?

If the reason #1 above didn't form a black hole is one of several explanations such as inflation or whatever else, then why didn't all the mass and energy form a big black hole at some finite time after this big bang happened?  For instance, I've (possibly incorrectly) heard that inflation made the universe the size of an orange.  Well why didn't it form a black hole then?  Or once the universe expanded to, say, the size of the moon. Why not then? Just insert whatever reasonable size you want in place of &quot;orange&quot; or &quot;moon.&quot;  The question is why didn't a black hole form out of all the matter and energy after the Big Bang?
Your problem essentially arises from trying to apply Schwarzschild black hole logic, the assumptions of which are pretty much maximally violated at the big bang.
The following were true at the big bang, and violate the usual black hole formation logic.
The event occurred everywhere in space, not actually a point. In particular, the energy was uniformly distributed everywhere. The net gravitational potential was therefore near zero, and there was no one point to which everything could collapse. Furthermore, since stuff was everywhere, there was no expanse of vacuum (in a flat spacetime, no less) outside the collapsing region. And furthermore, things were moving rapidly, were in a highly excited state, and were not in thermal equilibrium (until inflation hit, and then things were too diluted and causally disconnected to collapse en masse).
As for what we could describe the universe as at time $t=0$, we have no idea. General relativity has a spacelike singularity there, and it subsequently cannot say anything beyond that. It is expected that general relativity is not a correct description of spacetime in the pre-inflation era, in large part because quantum mechanics introduces significant effects in those conditions, and it is well known that the two theories are incompatible.
Edit:
This question has been asked on the physics SE many times.
https://physics.stackexchange.com/q/20394/55483
https://physics.stackexchange.com/q/3294/55483
https://physics.stackexchange.com/q/26435/55483
Perhaps the answers there will be illuminating.