Answering “where” is difficult because our human understanding of where tends to be relative to where in our universe, and that definition kinda falls apart at the Big Bang.
Kids in school are taught fairly simplistically that before the Big Bang everything was squished down into a single point, and then it all exploded outward, which is the basic gist of it, but it often leaves people with the idea that space existed somehow before that and it’s just all of the matter in it that was a single point and exploded outward. The idea of expanding space is a bit difficult for grade school kids to grasp, but understanding the expansion of space itself is key to understanding the nature of the universe and the Big Bang.
Let’s assume we have an imaginary flag, and we put it at some point in space, and that flag never, ever moves. It stays exactly where it is in the universe. Now we go some distance away and we place another imaginary flag, and that flag also never, ever moves. Both flags are completely stationary. What you find is that the distance between the flags is currently increasing. The flags aren’t moving. What is happening is that the space in between the flags is expanding.
The guy who figured this out was named Edwin Hubble, though like much in science, Hubble’s work was based on earlier work and ends up being related to the theory of relativity. Hubble got a telescope named after him, and the rate of expansion of the universe is now called the Hubble constant.
If you could go back in time, those two imaginary flags would get closer and closer. The flags still aren’t moving, but since space has constantly been expanding, the flags have been constantly moving away from each other (even though they aren’t actually moving), so going backwards makes the flags seem to get closer and closer. If you go back far enough those two flags meet at a point. In fact, all of the imaginary flags all over the universe all come squishing together at a point. That flag that was right next to you is now at that point. That flag that was 30 million light years away is now at that point. Another flag that is 50 million light years away in the opposite direction is also at that point. This is where the Big Bang happened, at that point. All of those flags, all of the “where” points in the universe, are all at one point. Since all of those little flags are all at the same point, this is what people mean when they say that the Big Bang happened everywhere. Every point in the universe was at that same point.
The “when” part of this, as was already answered, was about 13 to 14 billion years ago. 13.7 is the most commonly accepted number, but estimates vary a bit. The Wilkinson Microwave Anisotropy Probe (WMAP) came up with a number of 13.77. The Planck Collaboration came up with the number 13.82. All of those numbers are plus or minus a few hundred thousand years.
This leads to some interesting questions. If the universe is expanding, is it expanding inside of something? If so, what is that something? Are there other universes out there? What created the singularity that the universe expanded out of? At the moment, the answer to all of these is that we don’t have a freaking clue. For what it’s worth, Stephen Hawkings believes that there are other universes out there, and most folks consider him to be a reasonably smart guy.
Trying to take a step back and asking where and when did space and time happen is problematic because “where” and “when” are both terms that only apply to inside our universe. It’s kinda like having a sheet of paper sitting on your desk and having a ball sitting on the floor and asking where on the paper is the ball sitting. The ball isn’t sitting on the paper. And when and where spacetime began isn’t within our understanding of “where and when” as “where and when” only have meaning inside our universe.