I’m not going to present and defend any version of the cosmological argument here. I’ve done that at length in my books Aquinas and The Last Superstition, and it needs to be done at length rather than in the context of a blog post. The reason is that, while the basic structure of the main versions of the argument is fairly simple, the background metaphysics necessary to a proper understanding of the key terms and inferences is not. It needs some spelling out, which is why Aquinas and The Last Superstition each devote a long chapter to general metaphysics before addressing the question of God’s existence. The serious objections to the argument can in my view all be answered, but that too can properly be done only after the background ideas have been set out. And that too is a task carried out in the books.
Addendum: For two followup posts in reply to Jason Rosenhouse, go here and here.