The Universe began to exit is the 2nd premise of KCA. Since the Big Bang theory is NOT a theory of the origin of Universe[2a], it no longer holds much importance in Cosmological argument. Christian philosopher William Lane Craig argues that The Borde, Guth, Vilenkin Theorem[2b] acts as a empirical scientific evidence to establish the truth of this premise.
Victor J. Stenger in his most recent book, The Fallacy of Fine-Tuning[2c] :
The conclusion that Borde and collaborators had proved that the universe had to have a beginning was disputed the same year by University of California-Santa Cruz physicist Anthony Aguirre and Cambridge astronomer Steven Gratton in a paper that Craig ignores. Being good scholars, Borde et al. refer to Aguirre and Gratton in their own paper. I contacted Aguirre and Vilenkin, the latter whom I have known professionally for many years. I greatly admire the work of each, which will be referred to often on these pages. I first asked Vilenkin if Craig's statement is accurate. Vilenkin replied:
"I would say this is basically correct, except the words “absolute beginning” do raise some red flags. The theorem says that if the universe is everywhere expanding (on average), then the histories of most particles cannot be extended to the infinite past. In other words, if we follow the trajectory of some particle to the past, we inevitably come to a point where the assumption of the theorem breaks down—that is, where the universe is no longer expanding.
This is true for all particles, except perhaps a set of measure zero. In other words, there may be some (infinitely rare) particles whose histories are infinitely long."
I then asked Vilenkin, “Does your theorem prove that the universe must have had a beginning?”
He immediately replied,
"No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time."
Vilenkin further explained, "For example, Anthony in his work with Gratton, and Carroll and Chen, proposed that the universe could be contracting before it started expanding. The boundary then corresponds to the moment (that Anthony referred to as t = 0) between the contraction and expansion phases, when the universe was momentarily static. They postulated in addition that the arrow of time in the contracting part of space-time runs in the opposite way, so that entropy grows in both time directions from t=0."
I also checked with Caltech cosmologist Sean Carroll, whose recent book From Eternity to Here provides an excellent discussion of many of the problems associated with early universe cosmology. Here was his response:
"I think my answer would be fairly concise: no result derived on the basis of classical spacetime can be used to derive anything truly fundamental, since classical general relativity isn't right. You need to quantize gravity. The BGV [Borde, Guth, Vilenkin] singularity theorem is certainly interesting and important, because it helps us understand where classical GR breaks down, but it doesn't help us decide what to do when it breaks down. Surely there's no need to throw up our hands and declare that this puzzle can't be resolved within a materialist framework. Invoking God to fill this particular gap is just as premature and unwarranted as all the other gaps.
William Craig frequently quotes Vilenkin in his arguments although Vilenkin dismissed[2d] the existence of God as a cause of the begining of the Universe. But most recently in 11 january, 2012 in the New Scientist magazine[2e], Vilenkin argued for a begining of the Universe.
Alan Guth in his Cosmic Inflation paper[2f] wrote,
There is, of course, no conclusion that an eternally inflating model must have a unique beginning, and no conclusion that there is an upper bound on the length of all backwards-going geodesics from a given point. There may be models with regions of contraction embedded within the expanding region that could evade our theorem. Aguirre & Gratton (2002, 2003)have proposed a model that evades our theorem, in which the arrow of time reverses at the t = -1 hypersurface, so the universe “expands” in both halves of the full de Sitter space.