What is the name of prevailing cosmological model explaining the existence of the observable universe?

The Big Bang theory is the prevailing cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution.

After its initial expansion, an event that is by itself often called "the Big Bang", the universe cooled sufficiently to allow the formation of subatomic particles, and later atoms. Giant clouds of these primordial elements—mostly hydrogen, with some helium and lithium—later coalesced through gravity, forming early stars and galaxies, the descendants of which are visible today. Besides these primordial building materials, astronomers observe the gravitational effects of an unknown dark matter surrounding galaxies.

Georges Lemaître first noted in 1927 that an expanding universe could be traced back in time to an originating single point, which he called the "primeval atom". Edwin Hubble confirmed through analysis of galactic redshifts in 1929 that galaxies are indeed drifting apart; this is important observational evidence for an expanding universe.