In the 1920's, an astronomer named Edwin Hubble discovered something called "Red Shift." Basically, objects moving away from us have their light shifted toward the red end of the spectrum. Conversely, objects moving towards us have their light shifted toward the blue end.
When he looked out into the universe, he discovered that many of the galaxies were moving away from us; those that were the most distant seemed to be moving the fastest away, and those closer in, moving away a little slower. In explaining what he'd found, he said it was like "Fragments of a bomb."
If you consider what the universe was like earlier - since it appears to be expanding now, it must've been much smaller in the past. If we step backwards through time, it appears that the universe started from a small point, which expanded - space, time, and matter all came from this small point. *How* it happened - and why - are still being researched... but, this "Big Bang" seems to be the best fit for what we observe today. So - based on the observational evidence - it's the best explanation we have to the beginning of the universe.