Physicists used to think that the universe had existed forever—unchangingly, because that's what their observations of the night sky suggested. Needless to say, this view clashed with the "origin" or "creation" stories of most major religions, which hold that the universe had a beginning. So, it's not surprising that it was a Catholic priest, Georges Lemaître. Who was one of the first major proponents of a new scientific viewpoint—that the universe did have a beginning.
Lemaître, of course, was also an excellent mathematician and scientist. Based on his conviction not (just) on his religious beliefs but upon new experimental evidence from Edwin Hubble that showed the universe was expanding.
This evidence, combined with the mathematics of general relativity allowed Lemaître to "rewind" cosmic history and calculate that the farther back in time you go, the smaller the universe had to be. The natural conclusion is that everything we can currently see in the universe was at one point in time more or less at one point in space.
Lemaître called this idea the "Primeval Atom", but of course today we know it as "The Big Bang Theory". Except "Big Bang" is a horrible name—it would be much more accurate to call it "The Everywhere Stretch". Because one of the most common misconceptions about the Big Bang. The theory says that that the entire universe was compressed into a single point from which it then somehow expanded into the surrounding.
It is true that the observable universe, that is, the part of the whole universe we can see from Earth, was indeed shrunk down to a very very small bit of space. However, that bit of space was NOT a single point, nor was the rest of the Universe also in that same bit of space.
The explanation for this is the magical power of infinity. The whole universe is really BIG! Current data show it's at least 20 times bigger than the observable universe. However, that's just a lower bound —it might be infinite. If you have an infinite amount of space, you can scale space down, shrink everything to minuscule proportions, and still have an infinite amount of space. Kind of like how you can zoom out as much as you want from a number line. Furthermore, it'll still be an infinite number line.
Essentially, space doesn't need anywhere to expand "into" because it can expand into itself and still have plenty of room. In fact, this is possible even if space turns out not to be infinite in size, though the reasons are complicated and have to do with the infinite differentiability of the metric of space-time.
Anyway, the event unfortunately known as the Big Bang was basically a time, long ago, when space was much more squeezed together, and the observable universe, which is, everything that we see from Earth, was crammed into a very very small piece of space.
Since the entire early universe was dense and hot everywhere. Spacetime was curved everywhere and this curvature manifested itself as a rapid expansion of space throughout the universe. Although, people call this "The Big Bang", it wasn't just big, it was everywhere. It wasn't really an explosion—it was space stretching out.
It's really quite unfortunate that "The Everywhere Stretch" isn't nearly as catchy as "the Big Bang". This brings us to the “Big Bang Singularity”. This is an even horribler name because every single word is misleading. I mean, "Singularity" seems to imply something that happened at a single point. Which isn't at all what it's referring to—it should be called "The Part of the Everywhere Stretch.” Where we don't know what we're talking about."
Basically, our current physical models for the universe are unable to properly explain and predict what was happening at the very very beginning when the universe was super super scaled down. Rather than call it the "Time When We Don't Have a Clue What was Happening, ANYWHERE", for some reason we call it a "singularity".
This ignorance, however, does conveniently answer the question, “What happened before the Big Bang? Since it tells us the question isn't well defined—back when space was so incredibly compressed and everything was ridiculously hot and dense
Our mathematical model of the universe break down so much that time doesn't even make sense. It's kind of like how at the north pole, the concept of "north" breaks down—I mean, what's north of the north pole? The only thing you can say is that everywhere on earth is south of the north pole, or similarly everywhen in the universe is after the beginning.
However, once time began, whenever that was, space expanded incredibly quickly all throughout the universe—for a little while. Then expansion slowed, the universe cooled, stuff happened, and after a few billion years, here we are.
One thing we still don’t know is why this “Everywhere Stretching” happened? Why did the universe start off in such a funny, compressed state, and why did it follow the seemingly arbitrary laws of physics that have governed its expansion and development ever since?
For Georges Lemaître, this might be where God finally comes into the picture to explain the things science can't. Except that experimental evidence doesn't actually rule out the possibility that there may indeed be a time "before" the beginning. A previous age of the universe that ended when space collapsed in on itself, getting quite compressed and dense and hot
This is not enough to mangle up our ideas of “what time is?” It would have then bounced back out, stretching in a fashion similar to what we call the Big Bang. We don't know what we're talking about—singularity part.
So, physics may actually be nudging us back to the view that the Universe is eternal and didn't begin after all. In which case, Professor Lemaître might have to rethink his interpretation of the words "In the Beginning."