Here is Graham Oppys response to some Craig's claims about the Kalam argument.
Grünbaum (1990) (1991) worries about the propriety of the claim, that the universe began to exist, in the context of classical Big Bang models of the origins of the universe. In particular, he considers two cases: (i) models which are closed at the Big Bang instant t=0, in which t=0 is the location of a singular, temporally first event in the history of the universe; and (ii) models which are open at the Big Bang instant t=0, in which there is no singular, temporally first event in the history of the universe.
In connection with the first type of model, Grünbaum observes that it is misleading to say that in these models the universe began because this suggests that there were moments of time before t=0. Craig (1992:237f.) objects that "x begins to exist" should not be analysed as "x exists at time t and there are times immediately prior to t at which x does not exist", but rather as "x exists at t and there is no time immediately prior to t at which x exists." Of course, this analysis would commit Craig to the unwanted claim that God began to exist--since, on the theistic version of this model, there is no time immediately prior to t=0 at which God exists--so Craig further suggests that, within a theistic context, the analysis should be amended to "x exists at t; there is no time immediately prior to t at which x exists; and the actual world contains no state of affairs involving x's timeless existence." But this amended suggestion invokes the extremely puzzling notion of "(God's) timeless existence." Moreover, even the unamended analysis naturally provokes the question whether anything which begins to exist in this sense must have a cause.
Here's a key issue that comes up in Kalam debates. Does the idea that everything that begins to exist must have a cause of its existence hold up if there is, as standard BBT postulates, that there is no time prior to the first event.