"Assume" is the wrong word. "Assume" suggests that the theory is just a guess and only a handful of people, relative to all astrophysists, accept it as true.

In contrast, most, if not all astrophysists accept the "big bang" theory is very likely. And studies of light, matter, dark matter, stars, galaxies, the "arrow of time", entropy, and especially the Cosmic Microwave Background, suggests that the "big bang" theory is very likely.

Matter is actually all over the place. But 80%, or something high like that, is dark matter - a horrible name. It's only called "dark matter" because, we don't know what it is. We only know that it exists because of its effects on other structures (i.e. galaxies, and other space stuff). But it is "matter" - or whatever scientists eventually call it when they find out what it actually is.

Um, not really.

Essentially, if you extrapolate the movement of the galaxies back through time it resolves to a single point. Also, the CBR (cosmic background radiation,) which can almost be thought of as the remnants of the Big Bang "fireball" is extremely consistent with itself as well as the theoretical model that was developed prior to the CBR's accidental discovery.

The evidence supports one and only one Big Bang.