You're falling into the trap...
...of thinking that there is an "inside" and an "outside".
The Universe isn't expanding INTO something. The universe is ALREADY everything, AND it's expanding.
Every object in the Universe has moved, over time, away from every OTHER object (on average - there have been a few collisions and things on a local scale). There IS and WAS no "centre", and there is no reference point for the "original singularity". It originally had no size, now it is effectively infinite, since all of space-time is "trapped" in the Universe (or the Universe is trapped in space-time...)