The universe began with the Big Bang. This was the primal explosion that created energy, matter & space/time. While it is often called an "explosion," it was not an explosion in the ordinary sense. What happened was that space/time began expanding from a point called a singularity and in doing so carried energy and matter with it. Stuff did not explode into space, but space itself was created as the singularity expanded. Where the singularity came from is beyond the scope of science. Science does not concern itself with the existence or nonexistence of God. In a practical sense, the universe was self-creating.
Cosmologists believe the Big Bang occurred 13.8 billion years ago. The universe was hot and dense in the beginning, and energy and matter were interchangeable. Gravity, electromagnetism, & the strong and weak nuclear forces were one.
Evidence for the Big Bang:
1 Edwin Hubble showed the universe to be expanding, that galaxies are moving away from each other. It is easy to conclude that if galaxies are receding, they must have been closer in the past and at one point all together. Expansion of the universe is compared to blowing up a balloon with dust on it.
2 Georges Lemaitre, a Belgian priest, spoke of a primeval atom. This became the basis for the Big Bang theory.
3 George Gamow predicted that radiation from the Big Bang filled the universe.
4 Arno Penzias and Robert Wilson proved Gamow right when they detected Cosmic Background Radiation using a radio telescope. It is the afterglow from the Big Bang and comes from all directions.
5 The Cosmic Background Explorer (COBE) and the Wilkinson Microwave Anisotropy Probe (WMAP) mapped the Cosmic Background Badiation.
As the universe cooled, inflation took place. The universe grew while energy turned into matter. Protons and neutrons formed. The elements hydrogen and helium came into existence. Heavy particles evolved. As the universe expanded, structures appeared. A billion years on, there were stars and galaxies.
Before 1998, it was thought that gravity would stop the expansion of the universe. But observations of supernovas prove the expansion is accelerating rather than slowing. The force causing the acceleration is called dark energy. The universe will expand forever.