An article at
Craig on Vilenkin on Cosmic Origins quote Vilenkin as saying that "Theologians have often welcomed any evidence regarding the beginning of the universe, regarding it as evidence for the existence of God.......So what do we make of a proof that a beginning is unavoidable? Is it a proof of the existence of God? This view would be far too simplistic. Anyone who attempts to understand the origin of the universe should be prepared to address its logical paradoxes. In this regard, the theorem that I proved with my colleagues does not give much of an advantage to the theologian over the scientist. As evidenced by Jinasena's remarks earlier in this chapter, religion is not immune to the paradoxes of creation."
Indeed. Vilenkin has been pretty explicit on this point, even going so far as to write to Craig-
"Whatever it's worth, my view is that the BGV theorem does not say anything about the existence of God one way or the other. In particular, the beginning of the universe could be a natural event, described by quantum cosmology."
Which is no surprise, since all the BGV theorem purports to prove (if successful), is that an inflationary universe extrapolated indefinitely into the past must have a finite boundary to the inflationary region. Put simply, for any inflationary universe, the inflationary period cannot have been past-eternal. The inflationary period, not the universe. Which is why the BGV doesn't help Craig with his premise that the universe began to exist, and doesn't corroborate Christian creation mythology.
Also, it should be noted one last time that the BGV, along with other competing pre-Big Bang cosmological models, are highly speculative- and even Vilenkin admits as much. The BGV operates within a classical framework- and we know classisical physics breaks down pre-Big Bang, so it could well be the a fully integrated quantum theory of gravity completely invalidates it-
so far as it goes. Confidence one way or the other, particularly on the part of laymen not qualified to take sides in a
heated dispute between top experts in the field, is simply dishonest or delusional. But this is moot since, as we've noted repeatedly,
the BGV does not prove the universe began to exist.
And just to make things nice and crystal clear, here is the conclusion from the actual peer-reviewed paper-
Borde said:
IV. Discussion. Our argument shows that null and timelike geodesics are, in general, past-incomplete in inflationary models, whether or not energy conditions hold, provided only that the averaged expansion condition Hav > 0 holds along these past-directed geodesics. This is a stronger conclusion than the one arrived at in previous work [8] in that we have shown under reasonable assumptions that almost all causal geodesics, when extended to the past of an arbitrary point, reach the boundary of the inflating region of spacetime in a finite proper time (finite affine length, in the null case).
What can lie beyond this boundary? Several possibilities have been discussed, one being that the boundary of the inflating region corresponds to the beginning of the Universe in a quantum nucleation event [12]. The boundary is then a closed spacelike hypersurface which can be determined from the appropriate instanton. Whatever the possibilities for the boundary, it is clear that unless the averaged expansion condition can somehow be avoided for all past-directed geodesics, inflation alone is not sufficient to provide a complete description of the Universe, and some new physics is necessary in order to determine the correct conditions at the boundary [20].