That's where my brain starts a meltdown. I can't imagine "nothing" and its ability to have something expand into it. I've just got to accept the fact that I don't have the tools of a Hawking, drop this topic, and go back to thinking about sex.
The theory claims “space-time” itself is being created by the expansion. There is no space or time outside the expansion.
The alternative is to imagine that something can expand into some OTHER THING with no observable effect on that OTHER THING or the first thing.
Science is based on observations. If you don't observe a collision taking place as the expansion takes place, then it would be equivalent to saying, "there is nothing there".
When it was learned that light can consist of "waves", scientists set about to find out what was waving. They hypothesized the existence of the "ether" which was the unobservable and non-moving "stuff" of which space was made. The Michelson-Morley experiment showed that light is observed to move at the speed of light, c, regardless of the presumed direction of the earth moving through the "ether".