An Issue with Craig's Kalam Cosmological Argument

William Lane Craig's kalam version of the cosmological argument runs as follows:

(1) Everything which begins to exist has a cause.
(2) The universe began to exist.
(3) Therefore, the universe has a cause.

Using Big Bang cosmology, Craig proceeds to unpack why the cause referred to in (3) must be a Being similar to the God of classical theism. Also, because of the paradox of the cosmological singularity representing the beginning of time itself, Craig defends the following idea: That although time begins to exist at t-1, it nonetheless remains true that the universe is past-finite, and so requires a cause to begin. To retain the idea that God is timeless, Craig claims that the moment God chooses to create is simultaneous with the moment of time's creation. This is an ingenius explanation, and it sufficiently deals with the cause-and-effect issues surrounding such an argument. But I can't help but feel there's a deeper problem with the argument, and it's this: How could a timeless Being become temporal? The notion seems extremely counterintuitive, if not down-right contradictory.

If a Being is timeless, it seems to me it would have to be essentially so. Yet Craig's argument implies that God is only contingently timeless. How can this be? It seems obvious that timelessness entails changelessness, because change always entails change at a time. It won't do to merely appeal to the fact that t-1 also represents the moment of God's choice to create, because the issue still remains: How can a timeless Being become temporal without entering time at a time, regardless of whether he created that time. The process of becoming, what the scholastics called being in fieri, logically depends on time already existing. Yet God's process of becoming is somewhere between time and not-time, which seems absurd. I'm not sure how to reconcile this.