Here is an argument that it is possible for an infinite number of objects to come into existence by successive addition, contrary to William Lane Craig. I am not sure how far I find this argument convincing, but it seems to me to be pretty strong. It's inspired by an idea of Wes Morriston.
An alpha-widget is an entity that has the following property. As soon as an alpha-widget x is made, it spends a year playing the violin, and doing nothing else. At the end of that year, x makes an almost-duplicate of itself in half of the time in which x itself was made: the almost-duplicate is just like x, except that if x has the information that it was made in t units of time, the almost-duplicate has the information that it was made in t/2 units of time. And alpha-widgets are never destroyed.
I now claim that it is possible for an alpha-widget to be made over the period of a year. If it were made, there would be a potentially infinite but never completed sequence of alpha-widgets coming into existence: the first at the beginning of year zero, the second at year 1.5, the third at year 2.75, and so on. Since the spacing between alpha-widgets is always more than a year, because of that year of violin-playing, we do not here have any counterexample to Craig.
It would be difficult, I think, for Craig to object to this possibility. It doesn't violate his strictures against actual infinities. It does require laws of nature different from those of our world, or perhaps divinely mediated miracles, in order to overcome speed of light limits on the production speed of an alpha-widget.
But now consider a beta-widget. Recall that an alpha-widget would first play the violin for a year, and then would make an almost-duplicate of itself in half the time that it itself was made. A beta-widget does the same thing, but in opposite order: it first makes the almost-duplicate in half time, and then plays the violin for a year. Since the alpha-widget is not doing anything in that year of violin playing other than playing the violin (it's not, for instance, setting up a production line for its almost-duplicate), there is no reason to suppose that it would be harder for God to make a beta-widget in a year than to make an alpha-widget in a year. (And, yes, God can make things non-instantaneously if he so chooses.)
So, it should be logically possible to make a beta-widget in a year. But if a beta-widget is made in a year, then half a year later, it makes another beta-widget. That one, then, makes another in a quarter of a year. And so on. By the time two years are up, we have an infinite number of beta-widgets produced by successive addition.
I should, of course, note that while I think there are problems in the Kalaam argument's a priori argument for the finite age of the universe, its a posteriori argument may well be fine, and in any case there are other cosmological arguments that work just fine.