the Big Bang
Run the expanding universe backward like a film and everything crowds together: galaxies merge, space contracts, and the whole cosmos grows hotter and denser until, some 13.8 billion years ago, it was almost unimaginably compressed and blazing hot. That reversed film is the Big Bang. It answers the question the expansion forces on us, if everything is flying apart now, what was it like when it was all packed close? The name misleads: this was not an explosion at a point inside a pre-existing space, but the beginning of the expansion of space everywhere at once.
The Big Bang is not one event but a model of the universe's whole thermal history, built on general relativity and the observed expansion. As the scale factor a(t) grows, the temperature falls roughly as T proportional to 1/a, so the early universe passed through a sequence of stages set by falling temperature: a quark soup, then protons and neutrons, then the forging of the first nuclei in the first few minutes (Big Bang nucleosynthesis), then, at about 380,000 years, the release of the cosmic microwave background when atoms first formed. Three pillars support it: the expansion itself, the light-element abundances, and that relic radiation.
Be careful about the very beginning. The naive extrapolation to t = 0 gives infinite density, a singularity, but this only signals that classical general relativity has broken down and that a theory of quantum gravity is needed; the Big Bang model is trustworthy from a tiny fraction of a second onward, not literally at zero. There was also no 'outside' and no 'before' in any ordinary sense, because time and space are part of what the model describes.
At about one second old the universe was around 10 billion kelvin, hot enough that neutrons and protons interconverted freely. As it cooled over the next three minutes, that balance froze in and set the roughly one-to-seven ratio of neutrons to protons that fixed how much helium the cosmos would contain.
The Big Bang is a thermal history, not a bang: cooling sets the milestones.
The Big Bang model does not claim to explain the universe from literally nothing, nor to describe t = 0; it describes the hot, dense, expanding aftermath. The moment of origin lies beyond it, in the domain of quantum gravity.