I intentionally wasn't specific about the nature of the expansion, but fortunately it doesn't impair my argument one iota. Whether the void is void of space-time or jelly donuts is not the issue; the issue is void v. not-void (i.e. that which we call "universe").
Though it doesn't affect my argument, please point me to relevant articles where expansion of our universe is defined as expansion of space-time itself, as opposed to general, sub-lightspeed movement of matter away from the point of origin (e.g. galaxies moving away from the epicenter of the big bang).
And no cosmological theory I am aware of suggests that there is such an ominous void you mention in your post.
It's so simple, it's implicit, and there's nothing ominous about it. Worst case, it's highly uncomfortable for the "one big bang from nothing, ever, and that's it" crowd to deal with, so they don't. It requires no great leap of logic to realize that for something to expand, by definition it must extend itself to some state in which it previously wasn't.
Answer me this. Pick a point, any point, thirty billion light years from earth. Tell me what you find there. There is no such point, you say? What? Space time curves back on itself at the current universal limit, like the interior of a balloon? Oh, the point thirty billion light years away isn't defined until spacetime reaches it? Oh, I see, so universal expansion defines new legal points of existence as it goes, acting as a giant existence wavefront. And what, precisely prevents there being multiple such existence wavefronts (i.e. universal boundaries). Uh oh. Science can't do it. It can only see inside its own envelope. Tsk, tsk...that pesky philosophy again.