We know that the universe is expanding right now. We have general relativity, which describes gravity and also the geometry of space-time. This theoory describes an expanding universe, but was initially rejected by Einstein because of that fact.
If we follow the expansion back in time, we see that the universe would have been hotter and denser in the past. We can actually see the afterglow of this how period in something called the cosmic background radiation, which was predicted a decade before it was actually seen. Today, we use the small variations in that background to learn more about the early universe, in particular, the signature of how the universe was in the very first second is left on this radiation.
Next, the abundances of various elements such as hydrogen, helium, and lithium are predicted by the way the temperature decreasedas the universe aged. We actually measure these and they agree with the predictions.
All of this supports the Big Bang theory. It is an interconnected net of observations and theory that explains those obsevations. It is not someone just dreaming it up and proposing it to the world which takes it as fact.
Finally, it may simply make no sense to talk about 'before the Big Bang' at all. Time itself is part of the structure of the universe according to general relativity. As such, time itself began with the universe. So to ask what was around before time is rather meaningless. The analagous situation is to ask what is north of the north pole.