Motion either reduces to more basic principles or its doesn’t, and 2,300 years of experience hasn’t reduced it to anything other than Aristotle’s potency and act. Motion is thus either irreducible or Aristotelian. As Aristotelian, it gives rise to the First Way, but Plato gives his own “First Way” from an account of motion as irreducible. The bones are this:
What has motion from another moves from what has motion in itself.
What has motion in itself is alive.
It follows that whatever is not alive is moved by the living, and so what Plato called “soul” has a causal priority to motion in the visible world. But a soul prior to all the world would deserve to be called a god.
I haven’t studied Plato’s idea of “motion in itself” at length, but my best guess is that it is a motion that can account for its direction to a good, as opposed to either what either doesn’t move at all, or moves only because it is pushed or pulled, or (like radioactive decay or heat) radiates indiscriminately into whatever is around. Plato is trying to explain the relation of the natural world to some good (absent this, we’re committed to some sort of nihilism), and what we call natural motion isn’t capable of accounting for this.
Aristotle denied the possibility of something “moving in itself” when he argued that everything in motion was moved by another, which was the premise that St. Thomas put at the head of the First Way. But it’s interesting that either everything in motion is moved by another or it isn’t, and there is a supernatural mover in either case.