Since I've been reading about causes, one part of the debate that stood out for me was the fact that neither Carroll nor Craig tried to define "cause." In terms of the debate, this was undoubtedly wise: a long digression on the different definitions of "cause" would probably have lost most of the audience. But it was bad philosophy. Carroll tried to explain that, for a physicist, having a consistent mathematical model that comports with the experimental evidence is all we need. Any discussion of causes and effects will proceed from that model. Craig simply kept repeating his argument from incredulity: a universe can't just pop into being without a reason.
But certainly, how we think about causation affect our ideas on whether a self-contained universe needs a cause.
(By the way, this issue is independent of whether the universe in question has a beginning or not. While it might seem intuitively that a universe that begins is more guilty of "just popping" into existence, it has often been argued that a universe that is infinite in time is no less in need of some sort of external cause or explanation.)
On Hume's regularity view, causation is a matter of constant conjunction: to know that A causes B, we need to know that A is always followed by B. So what we need to do is to make lots of observations of deities, and if "Let there be light!" is always followed by a universe popping into existence, then we can conclude that gods cause universes.
On Wesley Salmon's analysis, a causal process is one that can carry some sort of a mark that transmits from the cause to the effect. It would seem, though, that if God is perfect, God is impossible to mark. Thus, we could never tell if a mark can be passed to the universe.
Another modern approach is to take causation to involve the transmission of a conserved quantity, like energy or momentum. But neither the theist not the atheist would claim that a universe that has a beginning in time was initiated by a transfer of pre-existing energy, so in this case there is no possibility of a cause.
On the Aristotelian-Thomian analysis, causation involves a potentiality becoming actuality, and an external cause is necessary to tip something into actuality. A universe is obviously possible (if it were impossible we wouldn't be here), so on this analysis an external cause is needed to make the universe actual.
So it seems possible, in principle at least, that both Craig and Carroll are right: differing definitions of "cause" may yield different conclusions about whether a self-contained universe requires a cause.