I came across this argument in the book The Nature of Space and Time, which is based on a series of lectures given by Hawking and Penrose. Although it relates to Penrose's Weyl curvature hypothesis (WCH), it does not depend on it, and that, to me, makes it a lot more interesting, since I wouldn't bet a six-pack on the validity of the WCH. As a preliminary, Penrose observes that (in my possibly inaccurate paraphrase): (1) The Big Bang was not a generic state. A generic Big Bang state would have had a large Weyl curvature, but the universe we see looks nothing like the one that would have resulted from such an initial state. Our Big Bang appears to have had a small or even vanishing Weyl curvature. (2) The evolution of our universe has led to a state with nonvanishing Weyl curvature. (At black hole singularities, we even have diverging Weyl curvature.) At the end of his first lecture, someone in the audience asks whether he thinks quantum gravity removes singularities. He says: What do folks here think of this? It seems pretty compelling to me, and yet the practitioners of loop quantum cosmology seem to be very convinced at this point that they're on the right track with models in which the big bang singularity is removed. Presumably he has his cosmic cyclic cosmology (CCC) model in mind here (this was in 1996). Although CCC no longer looks viable, that doesn't resolve the issue he raises, which seems pretty model-independent. The possibility that occurs to me is that the big bang singularity is removed by quantum effects, the entropy of the universe was minimized at the big bang, and there is time-reversal symmetry, so that the thermodynamic arrow of time was reversed in the universe before the big bang. Thermodynamically, the big bang would then look like an extremely unlikely thermal fluctuation, but presumably whoever set the boundary conditions of the universe got to choose to make it that way.