1. Changing things exist. (Premise)
2. Changing things exhibit potentiality and actuality. (Premise)
3. No potentiality can actualize itself. (Premise)
4. Either some pure actuality exists, or else there is an infinite regress of potentialities being actualized. (Implied by 1 - 3)
5. There cannot be an infinite regress of potentialities being actualized. (Premise)
6. Therefore, some pure actuality exists. (From 4 and 5)
The divine attributes of pure actuality may be inferred easily. First, pure actuality must be immutable and therefore eternal and indestructible, since only entities that exhibit potentiality can change (ceasing to exist would constitute a change). Secondly, pure actuality must be unique (one), for if there were more than one pure actuality, then there would be distinctions between them. However, to be distinct from actuality is to be non-actuality, in which case the latter does not exist anyway.
Other entities are distinct from pure actuality not by actuality, but by their varying levels of potentiality. Pure actuality must also be omnipresent, since there is no place that can exist apart from actuality. Finally, pure actuality must also be very powerful (if not omnipotent) in order to causally sustain all potentialities and their actualizations. We have, then, an argument for a purely actual, immutable, eternal, indestructible, omnipresent, unique and very powerful entity. If this isn't God, it's certainly very God-like.
Now, is the argument sound?
In defense of (1), we observe that changing things exist. An acorn changes into an oak tree, for example. This leads us to premise (2). The acorn is merely an acorn in actuality (what a thing is), but is an oak tree or something else in potentiality (what a thing could be).
What about premise (3)? Let's stick with the acorn analogy. The acorn cannot actualize its own potentiality to become an oak tree. Rather, it requires water, sunlight and soil, among other things, to sustain its change. If at any point these actualities are removed, then the acorn's actualization to become an oak tree will cease.
(4) is implied by (1) through (3), so the only remaining key premise is (5). Can there be an infinite regress of potentialities being actualized? The beauty of this argument is that it leaves the finitude versus the infinitude of the universe's past as an open question. Even if the universe's past were infinite, it would still be composed of finite intervals of time. Now, at each finite interval, it is impossible to start counting and reach infinity. This is because there will always and indefinitely be another number to count before arriving at infinity.
What this means is that the regress of potentialities being actualized at any finite time cannot be infinite. At each finite interval, the regress of sustaining actualizations begins anew, and since it is impossible to form an actual infinite by successive addition whenever one begins counting, it follows that the regress must be finite, in confirmation of (5).
Therefore, we are more than justified in believing in God or, at the very least, something very much like God.