Thomas Aquinas’ 1st way to the existence of God:
1. Some things are in motion (i.e. changing). (e.g. my water going from hot to cold, going from healthy to sick)
2. A thing cannot, in the same respect and in the same way, move itself: it requires a mover.
3. A regress of movers cannot extend ad infinitum (i.e. an infinite regress doesn’t actually solve the problem)
4. Therefore, there is an unmoved mover from whom all motion proceeds.
The key premise is 3. The idea behind the third premise is that you can’t give what you don’t have (formally or imminently); there must be something that actualizes each thing’s potential. If I get a book from Joe, Joe gets the book from Amy, and Amy gets the book from Alex, then I can’t give the book to someone else if Alex doesn’t have the book. Now suppose the passing of the book goes on to infinity. That is, there’s always a person behind the other person. But remember, you can’t give what you don’t have. If there’s no first person with the book, nobody gets it EVEN IF the series goes back ad infinitum. Likewise, EVEN IF there’s an infinite number of train cars, nothing gets the ball rolling if there’s no engine. Similarly, even if a spoon stretches outwards to infinity, it doesn’t change unless there’s something to change it.
The main objection is that Aquinas’ argument here (particularly his regress premise, which also shows up in his 2nd way and 3rd way) relies on a particular formulation of the PSR which is highly controversial
#Rebuttal to Aquinas’ 1st way #Response #Summary #1st way #Change #motion #infinite series #back to infinity #infinite chain #PSR #Principle of Sufficient Reason
Philosophy of Religion blog 
>The main objection is that Aquinas’ argument here (particularly his regress premise, which also shows up in his 2nd way and 3rd way) relies on a particular formulation of the PSR which is highly controversial
Yes; again, that’s why the PSR (the scholastic version, NOT the Leibnizian version) is foundational for all of Aquinas’ arguments. That’s why one needs to discuss it first before delving into these arguments. If existence need not be fully intelligible, then there’s no reason to posit God. Otherwise, it seems we’re in for the long haul!
>The key premise is 3. The idea behind the third premise is that you can’t give what you don’t have (formally or imminently); there must be something that actualizes each thing’s potential. If I get a book from Joe, Joe gets the book from Amy, and Amy gets the book from Alex, then I can’t give the book to someone else if Alex doesn’t have the book. Now suppose the passing of the book goes on to infinity. That is, there’s always a person behind the other person. But remember, you can’t give what you don’t have. If there’s no first person with the book, nobody gets it EVEN IF the series goes back ad infinitum. Likewise, EVEN IF there’s an infinite number of train cars, nothing gets the ball rolling if there’s no engine. Similarly, even if a spoon stretches outwards to infinity, it doesn’t change unless there’s something to change it.
Even your example here seems to confuse accidentally and essentially ordered causation. The example of the book, according to Aquinas, COULD go on infinitely into the past, since it is of accidental causation, meaning causation over time (another example being two parents giving birth to a child, and that child having kids, and so on).. It is the “present-focused” essential causation that cannot go on forever. Look at the example of the chain in a previous comment of mine for a better example of an essentially caused chain.