With their current mathematical models, cosmologists can confidently trace the evolution of the universe back to within the first fraction of a second of its existence (known as Planck Time - effectively the smallest unit of time over which any meaningful physical event can occur). After this point, they can reliably trace the expansion of the universe over a series of evolutionary stages, beginning with an incomprehensibly hot "plasma" stage, where temperatures were hot enough to prevent even the basic building-blocks of matter from forming and ending with the cool, lumpy universe of stars and planets that we live in today. The big bang can say nothing of what happened prior to the hypothesised "singularity" from which everything came into existence*, but the rest of the predictions made by this model are confirmed by empirical observations such as Cosmic Background Radiation (the afterglow of the big bang), the uniform expansion of the galaxies and Hubble's deep field observations. In other words, regardless of your theological disposition, the big bang theory (or at least something very similar to it) is the only available explanation for the present shape and structure of the universe.
But the original question goes a bit deeper than that. We aren't so much interested in what happened after the singularity, but rather what happened before it: in other words, what conditions preceding the big bang allowed the singularity to come into existence in the first place? The simplest and most honest answer to that question is that the cosmologists don't know**, but that's not to say that science doesn't have some very important things to say on the issue.
Firstly, it has to be noted that due to the conflation of time and space in the (empirically proven) theory of General Relativity, time itself did not actually come into existence until the moment of the big bang***. Therefore, to talk of a "time" that existed before the big bang is as meaningless as talking of a "place" that exists south of the south pole: by definition, both are impossible. Now it is true that there are speculative theories concerning the sort of conditions that may have predicated the big-bang singularity (M Theory and the Multiverse Theory most prominently), but at present the only hypothesis concerning the origin of the universe that is supported by available evidence suggests - unequivocally - that time did not exist and could not have existed prior to the big bang, and to talk of what preceded the big bang is therefore meaningless.
But the failure of the question doesn't end there. As with the question in the previous post, this question carries a hidden assumption for which there is simply no evidence: that - in the absense of some external force - "nothingness" is the fixed, default state of nature. While we have to be careful about presuming our universal laws to be "absolute" (such that they must hold "beyond" our universe as well), the findings of quantum physics can only be seen to completely undermine this assumption. As I have already said, "'nothingness' (i.e. a quantum state that is both unchanging and certain) represents an unstable and - above all - impossible state of nature" - i.e. "something" coming into being is inevitable. In posing the question, Williams also seems to presume that a quantum singularity (such as that which gave rise to the universe) cannot emerge ex nihilo without the intercession of some kind of powerful, creative agency, but fails to acknowledge that such particles do manage flash in and out of existence all the time in our universe without any sign of a cosmic creator. In fact, such "fluctuations" are not especially mysterious at all and are actually mandated by the inexorably indeterminate nature of quantum fields.
However, I do not want to give the impression that questions concerning the origin of the universe can be so effortlessly waved away. I have pointed out that particles in a vacuum seem to pop in and out of existence of their own accord, but neglected to mention that these particles are far smaller than the singularity required to account for the present amount of energy contained within our universe. If we were to presume that it is meaningful to talk of a time and place beyond the universe, the properties of which led causally to the creation of our universe, and presume that the laws which operate here are roughly the same as those found in our universe (a presumption made by string theory, but not necessarily by other multiverse theories), then an extremely unlikely (but not impossible) fluctuation of sufficient size within an inflaton field could theoretically generate the energy needed to create our entire universe. As Brian Greene notes:
"[A] tiny nugget, on the order of 10^-26cm across, filled with a uniform inflaton field - and weighing a mere twenty pounds - would, through the ensuing inflationary expansion, acquire enough energy to account for all that we see in the universe today." (Fabric of the Cosmos, p.313).
Now as I said, such a fluctuation is certainly possible (remember, such fluctuations - though almost always on a much smaller scale - are actually necessitated by the laws of quantum physics) but the odds are incomprehensibly small. The energy that the Greene mentions would have to be packed into an area approximately 300 trillion times smaller than and 100 million billion billion times heavier than a helium atom - needless to say, that'd have to be one hell of a fluctuation! In cosmology, answers that rely on an element of exreme luck tend not to last very long. The flatness of the universe, for instance, was once chalked up to luck but we now know that there is a good reason for the shape of the universe, and it has to do with the manner in which the early universe expanded (a topic I may breach in my next post). In any case, while this theory on the origins of the universe may rely on an extremely improbable event and doesn't completely answer the question posed at the top of this post, such theories do - at least - help in reducing the mystery involved, by breaking the problems down into smaller and less insurmountable ones. To again quote Greene:
"By no means does this [theory] answer Leibniz's question of why there is something rather than nothing, since we've yet to explain why there is an inflaton or even the space it occupies. But the something in need of explanation weighs a whole lot less than my dog Rocky, and that's certainly a very different starting point than invisaged in the standard big bang [model]." (Ibid.)
So as you can see, much work remains to be done by the sciences on this issue, but I hope that I've been able to convey the idea that the question as to how the universe came into being is not quite so mysterious or unsolvable as we might be inclined to think at first glance. The human mind is not well equipped to comprehend the deeply counter-intuitive nature of the universe on the smallest levels (i.e. quantum theory) and the largest levels (i.e. the age of the universe) and is therefore naturally drawn to supernatural explanations that invoke beings of far greater complexity and inexplicability than the very things they are invoked to explain in the first place. For that reason, perhaps the best thing we can say in response to this question - as with the one before it - is nobody knows, but that in itself does not make the existence of gods any more likely.
* The big bang is not a theory as to how the universe came into existence, but rather a theory as to the universe evolved: it can no more account for the existence of the initial singularity than evolution can account for the Earth's first self-replicators. Also, the term "big bang" is also something of a misnomer, as it details not the explosion of matter into space (as the name would seem to suggest), but rather the extremely rapid expansion of space-time itself.
** Which is not cause in itself, of course, to invoke a metaphysical explanation to account for the origins of the universe. Gaps in our scientific knowledge cannot automatically be construed as positive evidence for the existence of gods: that is a non-sequitur. If the cosmologists don't know what preceded the singularity, then the theologians certainly don't know. (See also final paragraph.)
*** Cosmological conceptions of time are deeply counter-intuitive and there is a strong temptation to reject the idea that there could not have been a "time" before the moment of the big bang. How, afterall, could a timeless particle (i.e. the initial singularity) give rise to a universe that is not itself timeless? The question is mindbending, but don't mistake its mindbending nature for scientific ambiguity: we know that the universe was caused by the temporal expansion of a potentially non-temporal particle and that simply isn't up for debate.
While positing the existence of such an "eternal" particle may sound like a case of metaphysical pleading, keep in mind that such particles are hardly rare. If, as Wittgenstein put it, "we take eternity to mean not infinite temporal duration but timelessness" (Tracatus 6.4311) then such eternal particles already exist in the form of photons and other massless particles, which travel through space-time for potentially many billions of years and yet do not age a single second the entire time.