The Big Bang didn't happen at a single point in space

A widespread misconception is that the Big Bang was an explosion from a single point that expanded into existing empty space. It wasn't. The Big Bang was the rapid expansion of space itself — all of space simultaneously. There was no 'outside' the universe for it to expand into. Every point in the early universe was the origin; there is no centre. This is why astronomers observe the universe expanding equally in every direction from wherever they look. The term 'Big Bang' was coined by cosmologist Fred Hoyle in 1949 as mockery of the theory — the name stuck even though he rejected it.

Source: Hawking, A Brief History of Time (1988)