Ok...The game we have to play is that this condition is predicted by general relativity, so the answer we have to find also has to come from within this theory. Obviously we cannot, and will not ever confirm such a condition experimentally so it is scientifically untestable.
General relativity, and in particular, Einstein's relativistic equation for the gravitational field, tells us that the global geometry of the entire 4- dimensional space-time continuum is governed by its content of mass-energy. Cosmologically, this means that at least two categories of global topology are possible based on the 'constant curvature' assumption. In other words, if we assume that the average density of the universe is the same from place to place ON AVERAGE, then this leads to a solution for the geometry of space-time which has the same degree of curvature from place to place.
There are exactly two categories of solutions. The first category is that of a finite space-time. Both its space-like and time-like portions of space-time have finite limits. The universe is born at the Big Bang, expands to a maximum radius, and then collapses in the Big Crunch. Throughout its 80 billion year duration, at each instant, there is exactly a finite volume of 3-dimensional space in existence. This volume stretches to a maximum number of cubic megaparsecs at the time of maximum expansion, then shrinks to zero volume at the Big Crunch.
The second category of solutions is that of an infinite space-time. Here, the universe is born at the Big Bang, and expands indefinitely. The catch in this category of solutions is that AT EVERY INSTANT the global topology of the universe in infinite. The universe is infinite today. It was infinite when it was 1 minute old, and it was infinite AT THE BIG BANG. A closed, finite universe cannot become an infinite one as it evolves, and a spacetime whose 3- dimensional space-like portion is infinite today, must have also been infinite when the Big Bang happened. This is demanded by general relativity.
With the Big Bang we see the third class of 'singularity' proposed by classical general relativity. The first class was the type of Singularity encountered, mathematically, inside non-rotating black holes. Schwarschild Singularities are point-like regions in space-time where the curvature of space-time becomes infinite. They are 'point-like infinities' in the classical, non-quantum mechanical version of general relativity. The second category is that of the Kerr Singularity or the string singularity. In this case, the condition of infinite curvature exists along a closed loop in the equatorial plane of a rotating black hole, or along the back of a cosmic string.
The Big Bang Singularity, represents a condition in which the space-time curvature becomes infinite, not at a point, or along a line, but within a 3- dimensional volume. This volume, moreover, is infinite. This is why the Big Bang is such an impressive event in physics, and why even the best popularizations of what it was like do not come close to describing all of its bizarre aspects.
The key thing to remember is that if the universe is infinite now, as observations strongly suggest, then its 3-dimensional volume HAS ALWAYS BEEN INFINITE, even a trillion trillion trillionth of a second after the Big Bang when the local curvature at each point in this space was infinite. The caviat is that few physicists believe, now, that a purely classical description of this event is meaningful. That's why there is a massive search underway for a quantum theory of gravity, which will eliminate all singularities by smearing them out in space-time, and replacing them by a very large, but finite, curvature.