How long ago was the Big Bang?
That’s an easy one—13.7 billion years ago. The universe is expanding, so all the galaxies are moving apart from each other, and if you extrapolate this backwards they all meet at a point 13.7 billion years ago.
There are several lines of evidence—the expansion of the universe, which was observed by Edwin Hubble in the 20s; you’ve also got the cosmic microwave background—there are certain isotopes which were formed during big bang nuclear syntheses (but that’s fairly technical)…but they all point to 13.7 billion years ago.
Back then the universe was an infinitely small, infinitely dense point. Just don’t ask me what came before that!