I find it best to think of our universe as a combination of dimensions. Absent any one of these dimensions this would be a completely different universe altogether.
Outside of our universe, the dimensions are not combined in the same way they are inside of it. Its entirely likely that they are all present and simply aren't combined or are combined in some other way, or maybe there are completely new dimensions that aren't in our universe at all. In any case, outside of the combination we happen to live in, we can't exist. We are a product of this combination as much as everything else in the universe is. Which means 'leaving' this combination is not possible. It isn't so much that there is 'nothing' outside of our universe, its that you would be nothing outside of our universe.
In my opinion, it is entirely likely that there are other combinations of dimensions that are identical to our own. But this is not nearly as likely as completely alien combinations that do not resemble our universe in any way and would be incomprehensible to us.
So, when I think of the beginning of time or space, I imagine these things had always existed, but just weren't combined until the big bang. That's a beginning in every sense of the word.