There has to be a lot of guess-work here. The basic idea is that early university expanded very quickly from some hypothetical point, with lots and lots of energy that went on to form matter (here we get to the idea that matter and energy can be interchanged, at least under extreme conditions). One strange thing is why there is such asymmetry in the universe – why didn’t it all spread out evenly. The key explanations here relate to an idea called quantum mechanics – that one very small scales (the early universe must have been small for some very brief instant) there is a degree of randomness (a bit like rolling a dice to see what will happen), so this can lead to asymmetry – some bits of space were “lucky” enough for matter to form in, others weren’t. Lots of tricky and controversial Physics here!
By the way, be can still detect the afterglow of the big bang (“if it really happened” – I accept that your qualification is necessary!) in the radiation called the “cosmic microwave background”.
The big bang is really a term that describes the cooling and expansion of the universe, so during and after the big bang things would be getting colder! Also lots of energy was emmited which went on to form matter. Now, and this is where I can get lost, matter and energy are interchangable under extreme conditions and there would have been extreme conditions during and after the big bang.
ok – not my area but I’ll do my best to give you an answer.
About 13 to 14 billion years the universe was extremely hot and dense and under extreme pressure. It began to cool and expand exponentially. During this (incredibly short time) protons, neutrons, electrons and positrons developed.
After a few minutes, the temperature was down to about a billion degrees centigrade and neutrons combined with protons to form deuterium and helium nuclei, (lots of protons left over made hydrogen nuclei).
After 379,000 years the electrons and nuclei combined into atoms of hydrogen.
Slightly denser regions of matter attracted nearby matter and grew even denser forming gas clouds, stars and galaxies.
This theory is based on the fact that distant galaxies are speeding away from us and the further away galaxies are the faster they’re going. If the distance between galaxys is increasing today, everything must have been closer together in the past.