I guess the standard answer to this question goes something like this:
The Big Bang event did not have a boundary - put simply, the event created the dimensions it occupied as it happened. The question is similiar
to the old philosophical argument regarding what exists "outside" the universe - since the entire universe was created by the big bang, it may help
to visualise the event as an unfolding of an infinite space into three dimensions, rather than a fireball "Hollywood" explosion.
This hints at a wider problem - namely, the reliance on metaphor and imagery when describing events which do not necessarily conform to the physical
laws as we understand them. Size, shape, distance, time - all these concepts were irrelevant (nonexistant?) at the moment of the Big Bang.
Anecdotally, I once had a friend who, when faced with the Big Bang, the concept of infinity, and particularly string theory, decreed that he could
only understand them when drunk or stoned.
Duuuuude, physics *rocks*!