You're kind of right. We live in the expanding cloud of the "explosion" (not an explosion) and everything we can see and measure is really just facets and manifestation of that explosion (not an explosion) that could be just as easily though of as "ripples" as anything else.

Now, whether we're expanding "into" anything, or across the surface of anything is anyone's guess. We don't really know what lies beyond / below the universe, whether there's some larger "structure" that hosts the multiverse or not. M-Theory says there is, but we haven't any experiments to verify M-Theory, at least, not yet.