“The world you see, nature’s greatest and most glorious creation, and the human mind which gazes and wonders at it, and is the most splendid part of it, these are our own everlasting possessions and will remain with us as long as we ourselves remain.” -Seneca
Asking where in space the Big Bang happened is like asking where the starting point of Earth’s surface is. There’s no one “point” where it began, unless you’re talking about a point in time. The reality is that, as far as space is concerned, the Big Bang occurred everywhere at once, and we have the evidence to prove it.
If the Big Bang were an explosion, we would discover ourselves in a Universe that had a preferred location with different densities surrounding it, but instead we see a Universe that has the same density everywhere. We’d see a Universe that looked different in different directions, yet we see one that’s uniform to better than one part in 10,000 in each direction we look. And we see a Universe that exhibits zero spatial curvature: one that’s indistinguishable from flat.