Don Lincoln, from Fermilab, a real scientist, as opposed to the characters from The Big Bang Theory, explains what the Big Bang theory actually is and why it has been proven until now. There are three points that lead to a conclusion that the Universe started as a given time and in a given place: the accelerated expansion of the Universe, the presence of 92 atoms of hydrogen for every 8 atoms of helium and the cosmic background radiation.
Hubble discovered the expansion of the Universe in 1929, then Ralph Alpher, Hans Bethe and George Gamow have explained in 1948 that, for a big bang to exist, we need to have a specific proportion for the main elements in the periodic table of elements: 92 atoms of hydrogen for every 8 atoms of helium. Finally, in 1964 scientist have discovered that every point in space has at least 2.7 degrees K and no less due to the cosmic background radiation, a remnant of the Big Bang. Arno Penzias and Robert Woodrow Wilson were the discoverers of the CMBR as they experimented with the Holmdel Horn Antenna.
Also, the big bang was not big, neither a bang and it neither occurred from a single point. It was an everywhere stretch, the entire Universe stretched like crazy: