Unmoved Mover and Proof of God?

I guess many of us will be vaguely aware of talk of God as Unmoved Mover or Uncaused Cause and maybe even of this as an argument for the existence of God: if stuff exists or changes, it must have a great Maker or one who affects it. 

Edward Feser puts forward what he calls an Aristotelian Proof for the existence of God both more informally and then more formally (in 50 points). This argument is that real change exists. It is the actualization of potential. And this is not possible unless there is something that can actualize without itself being actualized, a purely actual actualizer (Five Proofs of the Existence of God, Ignatius Press, 2017, p12). 

One thing that strikes me about this is that he argues not just for some great powerful creator. He argues that a purely actual cause of the existence of things which is immutable, eternal, immaterial, incorporeal, perfect, fully good, omnipotent, intelligent and omniscient is required (p37). In other words, the God of classical theism must exist. 

And this is only one of his five proofs. He also offers:

(2)  a neo-Platonic (composition / parts require One simple cause) 

(3) Augustinian (universals must exist in the mind of God)

(4) Thomistic (nothing could exist unless there exists a being whose essence is existence) and 

(5) rationalistic proofs (the principle of sufficient reason requires a necessary being the existence of which must be explained by its own nature). 

Feser argues that none of the objections to these arguments succeeds "and indeed that the most common objections are staggeringly feeble and overrated."

He says: "This is a confident claim, I realize. But natural theology, historically, was a confident discipline. A long line of thinkers from the beginnings of Western thought down to the present day - Aristotelians, Neo-Platonists, Thomists and other Scholastics, early modern rationalists, and philosophers of some other schools too, whether pagans, Jews, Christians, Muslims, or philosophical theists - have affirmed that God's existence can be rationally demonstrated by purely philosophical arguments. The aim of this book is to show that they were right, that what long was the mainstream position in Western thought ought to be the mainstream position again." (p15)