Commonly accepted theory which describes the origin and evolution of the Universe is the standard cosmological model, called also the Big Bang theory. 

At the very beginning the temperature and density was infinite. 

In fact we can’t say if this moment really happened, to say nothing of initial conditions. But after 10^-12 second (!) the temperature was low enough (10¹⁵ degrees !) to make use of our physical theories. The space was filled with gas, that consist of all known elementary particles and their antiparticles created and annihilated in collisions. The Universe have been rapidly expanding and cooling. Creation became slower that annihilation and almost all particles and antiparticles disappeared. A little surplus of matter over antimatter (about 1/10¹⁰) formed during first few minutes light elements atomic nuclei. Neutral hydrogen atoms originated after 300, 000 years. At this time the Universe became transparent.

 It is assumed that the Universe was homogeneously filled with matter, however there had been little clumpiness, that later formed galaxies and stars. When the Universe was half its present size most of the heavy elements were created.  Our Solar System originated 5 billion years ago, when the Universe was two third its present size. 


 Big Bang was not an explosion in a specific point in space, after which some parts were moving faster into emptiness. Galaxies do not become bigger. It’s the space that is expanding.  Particles uniformly fill all space and average density constantly decrease.
 "the expansion is similar to a rising loaf of raisin bread. The dough expands, the raisins move apart. Moreover, the speed with which any two raisins move apart is directly and positively related to the amount of dough separating them." (J. Peebles "The Evolution of the Universe" p.30 Scientific American October 94)