That's a laughable notion. One would presume that Hawking has no problem with infinities in space, so why should his cosmology stumble over an infinity in time?
Or, to put it another way, our current cosmology (for this universe, at least...in itself a curious notion...) traces back to a singularity of infinitely dense, infinitely hot matter at time T=0. What makes this idea any less metaphysical than the idea of the existence of a time T=-1 femtoseconds?
Hawking just has a hang-up about infinite time.