Here's an argument of Craig's:
1. Everything that begins to exist has a cause of its existence (Why? “It is based on the metaphysical intuition that something cannot come out of nothing.”).
2. The universe began to exist (Why? Forget the conceptual arguments, our best science is supposed to show that there was a first moment).
C. The universe has a cause of its existence (“Given the intuitively obvious principle that whatever begins to exist has a cause of its existence, we have been led to conclude that the universe has a cause of its existence. On the basis of our argument, this cause would have to be uncaused, eternal, changeless, timeless, and immaterial. Moreover, it would have to be a personal agent who freely elects to create an effect in time. Therefore, on the basis of the kalam cosmological argument, I conclude that it is rational to believe that God exists.”).
We can worry a bit about the scientific rationale for (2). As noted by Oppy, John Earman claims, “in standard Big Bang models, for every time t there is an earlier time t’, and the state of the universe at t’ is a causal determinant of the state of the universe at t. Thus, it turns out that, even in the standard Big Bang models, there is no ‘absolute beginning’ of the physical universe.” Bracket this. Let's suppose we can place a lot of confidence in the Big Bang Theory and let's suppose that we can say that the theory is properly interpreted in such a way that it posits a first moment. Everitt thinks there's no cause for concern. In The Non-Existence of God he writes:
What about the universe as a whole—could it have a cause? There is a straightforward reason for saying that the universe as a whole could not have a cause. Recall that the phrase ‘the universe’ is here being used to include space and time as well as matter. This means that there could not have been an event preceding the universe and bringing it about, for the simple reason that there was no time before the start of the universe in which that even could have occurred. If per impossible there had been any event before the supposed start of the universe, that would simply show that the universe had in fact begun earlier than we had assumed (70).
But, it seems he's denying (1) and (1) strikes many as being completely obvious. It's as if Everitt is saying that really something can come out of nothing. Let me try to put the point differently, but in a way that I think is very much in the spirit of what Everitt is saying.
Hank Williams (begat) Hank Williams, Jr. (begat) Hank III
This diagram represents time and the Hanks. According to (1), if Hank Williams, Jr. began to exist, he has a cause. We know that Hank Williams, Jr. began to exist because there are times at which he does not exist that precede the times at which he does exist. So far, so good. So, it seems that the principle allows us to infer that there was a cause. In this case, the cause is Hank Williams.
According to (2), the universe began to exist. So, it seems that according to (1), the universe had a cause. Something begat the universe just as something begat Hank III, Hank Williams, Jr., etc…
Note, however, that there are two reasons to say that the Hanks began to exist:
(i) They have existed for a finite duration.
(ii) There were times at which they did not exist prior to the times at which they did exist.
There is, however, at most only one reason to say that 'the universe' began to exist. So as to avoid any potential confusion, let’s distinguish two senses of ‘beginning to exist’. If something has existed for a finite duration, let’s say it had a ‘beginning-1’. If something is such that there are times at which it did not exist that precede the times at which it does, let’s say it had a ‘begnning-2’.
(Q) In what sense should we say that the universe had a beginning? Beginning-1? Beginning-2? Both?
(Q2) In what sense should we say that everything that begins to exist has a cause? Beginning-1? Beginning-2? Both?
Here is Craig’s motivation for the principle that everything that begins to exist has a cause: it is based on the intuition that, “something cannot come out of nothing”. That sounds like he’s concerned with beginning-2. Supposing that there is a first moment, in what sense does our best scientific theory (allegedly) show that the universe had a beginning? That sounds like beginning-1. I take it that Everitt’s point is that if we read the metaphysical principle as applying to things that began-1 but did not begin-2, the principle is false. If that’s not what it means and it applies only to things that begin-1, it doesn’t apply.