So, based on similar reasons as what you, @pevaquark, Aron Wall and others have pointed out, I agree that using the BGV theorem alone is not a good argument for arguing that the Universe had a beginning. This could be the impression left by many Christian apologists including Craig himself in some of his debates. However, Craig’s advocacy of the Kalam Cosmological Argument (KCA) goes back much further than the BGV theorem, and his contemporary version of it goes far wider than simply citing the BGV theorem. I think Matthew is not representing it fully. It is certainly not a naive argument for the existence of God.
The most recent version of Craig’s KCA is (I think) the essay in The Blackwell Companion to Natural Theology, coauthored with James Sinclair. Here, they marshall a wide set of arguments to argue for the finitude of the past. The first two are philosophical arguments: 1) Arguing that the existence an actual infinite is impossible, and 2) Arguing that the formation of an actual infinite through successive addition is impossible. I think these philosophical arguments have been developed by Craig since the 80s.
The third argument is the scientific one. Here, Craig & Sinclair’s argument is quite comprehensive, starting from the history of Big Bang theory. (Perhaps it would be interesting for you to read this complete article, as someone trained in GR and cosmology.) Before the 1920s, most physicists assumed that the universe was eternal and static. After Big Bang theory caught on, this no longer was the case - we can say that the universe is about 13 billion years old, and it included a singularity in the past, as C&S argue, due to the Hawking-Penrose theorems. C&S then talk about the exceptions to the H-P theorems, including eternal inflation, for which BVG is relevant. However, they also talk (with considerable technical detail) about quantum gravity models, including Pre-Big Bang inflation (Veneziano & Gasperini), ekpyrotic/cycling (Steinhardt & Turok), loop quantum gravity models, and Hartle-Hawking. For each of these models they argue that a beginning is required.
After C&S establish that a beginning is required, and that things which begin to exist have to be caused, they also talk about what kind of causal agent could have caused that. They argue that the First Cause must be beginningless, changeless, immaterial, timeless, spaceless, personal and enormously powerful. It is not merely saying “God did it”.
What do I think about all of these arguments? I think that C&S have done almost as much as is possible with current cosmological knowledge to argue that the universe must have had a beginning. BVG is spoken of a lot, but it is far from being the only thing they utilize. From an experimentalist point of view, none of these quantum gravity models have experimental corroboration yet, so I think that general scientific caution and skepticism is warranted. However, I think making a philosophical argument for the existence of God based on these comprehensive arguments is legitimate, even if I think they are not very strong arguments because we have very little knowledge about quantum gravity. (Assuming what C&S say about the science is correct. I am not sufficiently trained in GR & cosmology to judge that.)