Our solar system occupies a minuscule part of the galaxy we call the Milky Way. There are millions of such galaxies. In 1929, the American astronomer, Edwin Hubble, proved that the galaxies are moving apart from one another at tremendous speeds.
Scientists had known this at least a decade before Hubble proved it. In 1922 a Russian mathematician, Alexander Friedmann, had pointed out that if the universe was expanding because the galaxies were moving apart, the galaxies must have been closer to each other a hundred years earlier, still closer a thousand years earlier, still closer a million years earlier, and at one time they must have all been part of one great mass.
In 1927, a Belgian astronomer named Georges Lemaitre who was unaware of Friedmann's work came to the same conclusion as the Russian. He called the original mass from which all the galaxies took birth, the cosmic egg. He said the cosmic egg had exploded, flinging all its matter out, and the fragments (galaxies) were still moving apart because of the force of that explosion.
The theory was popularised in the 1930s and 1940s by the Russian-born American scientist George Gamov. He gave the primeval explosion the name 'Big Bang' and the theory came to be known as the Big Bang Theory.
The Big Bang theory does not explain how the cosmic egg and therefore the universe came into being. It only offers an explanation for the present state of the universe.