Right after the Big Bang, how did particles overcome extreme gravity and other forces and manage to fly apart? I have read this question:
Why did the universe not collapse to a black hole shortly after the big bang?
where Lubos Motl says:

This matter has no center - it is almost uniform throughout space - and has high enough velocity (away from itself) that the density eventually gets diluted.

Now this and none of the other (there are a lot) answers answer my question specifically. I am not asking about collapse into a black hole. I am asking, right after the Big Bang, the density was extreme, thus gravity and curvature had to be extreme, maybe the escape velocity (meaning in this case the velocity needed for particles to fly apart) could have reached close to or even exceed the speed of light. But that is just gravity. There are the other forces (at that point unified if I understand correctly), that must have been holding particles together. This could involve the photon and the quark epoch as well.
Now first I thought:

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*Maybe it was not particles flying apart, but simply just space expanding between them. But wait. First of all, space is expanding even now. Everywhere. Contrary to popular belief, space is expanding everywhere. Even here where we are. It is just that here, the other forces are dominating. Us, who are made up of matter, are held together by the other forces, that dominate over space expansion. So space is expanding right here, but the matter we are made up of stays together. No flying apart here. Space was expanding back then too. then how was space expansion able to overcome all the other forces back then but not now?


*It might be just a scale issue. Space expansion, some call it dark energy, might just be some kind of force, negative pressure, that is spread over the whole universe. It acts only on large scales. For now. But when the universe was extremely small, the scales were small too, and maybe dark energy was concentrated onto this small region, making it relatively stronger compared to the other forces.
Question:

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*Right after the Big Bang, how did particles overcome extreme gravity and other forces and manage to fly apart?

 A: There are two reasons why there was no gravitational collapse in the very early universe:

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*The distribution of energy and matter soon after the big bang was very nearly uniform. Because of this symmetry there was no reason for gravitational collapse to happen in one place rather than another - the net gravitational force at each location netted out to something very very close to zero.

*The early universe was at a very high temperature, which meant that fundamental particles were moving quickly, and gravity had very little effect on them.

Space was expanding, but this was not "overcoming" gravity. In fact, the expansion of space meant that the universe was cooling down, which assisted gravity. Like a pencil balanced on its point, the universe was in a state of unstable equilibrium, which became more unstable as it cooled.
As the universe expanded and cooled, fundamental particles combined into protons and neutrons, and then into atoms (almost all of which were hydrogen and helium atoms). This took several hundred thousand years. The very small deviations from absolute symmetry were then enough to trigger the collapse of the cooling atoms into gravitationally bound clouds, and then into the first stars and galaxies. But this process was very slow, and the first stars (called Population III stars) took hundreds of millions of years to form.
A: Is it being assumed in the above explanations that a dimensional "space" existing as a certain volume of vacuum (i.e., having or containing a complete absence of matter or energy) must have pre-existed the Big Bang events?  That seems like a very large assumption.
A: I think your question is based on a incorrect assumption about the geometry of the universe. You say that you are not asking about a black hole, but my guess is that you see the geometry of the universe a finite collection of matter surrounded by vacuum. If at an early time the temperature of this configuration of matter is not hot enough (or equivalently it does not have enough pressure), then all of the matter would collapse into a black hole.
If I am wrong about your view of the geometry, please let me know, and I will try to answer your question based on the actual geometry you have in mind. Is it finite or infinite? Is it homogeneous or something else? If finite, do you see it as a 3D boundary of a 4D hyper-sphere, or something else? Is dark energy present or not?
BTW: The expansion of space does not cause all matter to move apart, like very distant galaxies move away from the Milky Way. The matter in the Milky Way remains within a range identical to (or almost so) as it is now.
