I don't agree. If the Big Bang was something from the inside of the singularity outward then it existed within the singularity.
If it was simply the outside of the singularity opening up and allowing the contents to rush into nothingness then the outside of the singularity existed though it was maintaining time within itself. The inner surface of the outside of the singularity existed where time was contained. Therefore, it existed no matter if time was within the singularity or outside of it.
Unless, at the instant of the big bang, it wasn't a singularity, but an infinitely dense universe. The initial inflation supplied the space for density to drop. There may never have been a boundary that would mark the edge of the universe. Or, if space itself came into existence at the initiation of the big bang, again, there could be no limit because there was non space in which to have a limit.
There was no "surface" to exist in or that had an outside. There was nothing outside as space itself was created at the time. There was no "before" either as time too was created along with space.
What is this 'time' that can be contained with surfaces of something? What is this something?