Has the big bang theory been proven

The Big Bang Theory can never be certainly proven, simply because there was no one around to witness it. However, there is some very strong Evidence supporting it. There are only two ways to go: Either the Universe has always existed, or it had a beginning. Very strong evidence points to the latter.

Proof the Universe is Expanding
First and foremost, the Universe is expanding. This has been known for decades. Every galaxy outside our Local Group is speeding away from us. Imagine putting raisins in cake dough. As the yeast makes the cake rise, it expands and the pieces of raisin move further away from each other. This is what we observe with galaxies.

As galaxies move away from us, this causes their light to be shifted towards the red end of the spectrum, and the farther away they are from us, the greater the red shift. It's true that there are some galaxies as far away from us as the Virgo cluster that are approaching us and thus have a blue shifted spectrum, but those are merely because of these galaxies motions within their parent clusters. Moreover, there is a direct relationship between a galaxy's velocity away from us, it's red-shift and it's distance from us.

More proof came when quasars were first observed. At first, astronomers couldn't make sense of their spectra because they didn't appear to match any of the chemical elements. Then they realized they're showing even greater red-shifts than the galaxies they were studying, and the spectra they took were actually that of ionized hydrogen. Today there are many quasars known that are moving away from us at 90 percent of the speed of light, and light that is normally in the far ultraviolet and x-ray region of the spectrum has been shifted into the visible range. So there is proof that space itself is expanding, and moreover examination of supernovae in distant galaxies is showing that expansion is also accelerating. These supernova in distant galaxies are fainter than they should be based upon current theories, indicating that the Universe rate of expansion was not constant over it's lifetime. Today, dark energy and dark matter are vying for dominance, and it's dark energy that is forcing space to expand at an accelerating pace.