It is certain, and evident to our sense, that in the world some things are in motion. Now whatever is moved is moved by another, for nothing can be moved except as it is in potentiality to that towards which it is moved; whereas a thing moves inasmuch as it is in act or actuality. For motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be moved from a state of potentiality to actuality, except by something in a state of actuality... it is therefore impossible that in the same respect and in the same way a thing should be both mover and moved i.e. that it should move itself. Therefore, whatever is moved must be moved by another. If that by which it is moved must itself be moved, then this also needs to be moved by another, and that by another again. But this cannot go on to infinity, because then there would be no first mover, and consequently, no other mover, seeing as subsequent movers move only inasmuch as they are moved by the first mover; as the staff moves only because it is moved by the hand. Therefore it is necessary to arrive at the first mover, moved by no other; and this everyone understands to be God.
This is straight from Aristotle. Note that by “motion,” Aristotle and Aquinas really mean something broader, including growth and diminution. All movement is initiated, according to Aristotle’s axiom, by some prior moving thing; motion cannot suddenly happen by itself “ex nihilo.” This means motion is either an infinite regression, or there is a first, unchanging changer or unmoved mover, responsible for setting the whole chain reaction off. An infinite regression is logically impossible; therefore there exists some unmoved mover.
This unmoved mover seems to me to correspond most directly to the Christian concept of the Holy Spirit.
It might be objected that sentient beings do, indeed, move themselves, at least in some respects. Aristotle counters this by claiming that, in such cases, one can isolate a part, already in motion, moving the whole, and this part does not initiate its own motion or change. So the unmoved mover must still be postulated. I expect this is true in a purely physical sense; you never see a living thing emerge from something completely without motion, growth, or diminution. And a living thing is constantly in motion, in some part.
I think Aristotle’s proof can be related directly to the more modern theory of inertia. A body in motion will stay in motion; a body at rest will stay at rest. “When no external force is acting, a body at rest remains at rest and a body in motion continues moving in a straight line with a uniform speed.”
Therefore, for any motion to exist now, there must have been some initial injection of motion into the cosmos, by some “external force.”