Burn me for heresy, but it intuitively seems to me that if there was no time (i.e. nothing was changing) the "universe" would be in a state of equilibrium. Therefore, some external force would have to be present in order for the state of "matter" to change, and therefore "start" the flow of time? Am I making sense here?
If the universe was packed into an "infinitely" dense space, its own gravitational pull would be enormous, of course. Wouldn't you need an equally infinite force to disrupt this equilibrium? Or would force not even exist, because time did not exist, and force has a time component?
Ok, to start this off, I don't have that much knowledge on the subject, so part of what I'm saying is just my own speculation. That said, lets consider your first point. Is a universe without time really in "equilibrium." I'm personally inclined to say no. Why, you ask? Equilibrium mandates that something must cause it to change. However, without time, there can be no "cause and effect" as we know it. Cause implies something which happened before, and as a result of that cause happening, the effect happens at a later point
in time. If there is no time, therefore, there can be no cause and effect; so, it's impossible for the start of time to have a cause as we understand the term.
It's also entirely possible that the start of the universe was a random event, such as quantum events. We know that there is
NO CAUSE whatsoever for a quantum event. Therefore, when the entirety of the universe was squished together to within a quantum distance, it seems entirely possible for that universe to begin expanding at random, without any cause.
Now, as to your next question, you're entirely right that "before" the big bang, there was no time, and therefore no force. However, let's consider the moment right after things started existing. You are entirely right that the gravitational force would be nearly infinite. However, you also have to understand that stuff really doesn't like being squished that close together. You end up getting particles in the same quantum state, which can't actually happen in the universe that we know today, save theoretically in black holes. If, therefore, you cram the entire universe into that small of a space, there's going to be a force (I can't remember if it's the strong or weak nuclear force) which would push back against gravity with as much if not more force. Hence space can start expanding.
There's also the matter of dark energy which drives the expansion of the universe, but as I said before, it's only theoretical. A bunch of scientists said that "well, we don't know what's causing this within the known rules of physics, and the only way it can be explained within those rules is some energy we can't detect in any other way." Don't get me wrong, that's the same argument scientists used to find Neptune when Uranus's orbit didn't fit with the theory of gravity, so I do think it highly likely that dark energy exists. It's just that, by definition, we can't really know anything about it, save that it helps the universe expand.
Pre-edit: And yes, Armok's links do have helpful information. For example, the
Planck epoch is the first moment of time, where these things would have happened. What I didn't know before that I discovered reading the article is that it's entirely possible that all the forces in the universe were probably unified at that time. This would instantly cover the problem of gravity, though the differentiation occurred in the planck epoc, so I'm not too sure myself.