… Take Aquinas’s Second Way, for instance:
The second way is from the nature of the efficient cause. In the world of sense we find there is an order of efficient causes. There is no case known (neither is it, indeed, possible) in which a thing is found to be the efficient cause of itself; for so it would be prior to itself, which is impossible. Now in efficient causes it is not possible to go on to infinity, because in all efficient causes following in order, the first is the cause of the intermediate cause, and the intermediate is the cause of the ultimate cause, whether the intermediate cause be several, or only one. Now to take away the cause is to take away the effect. Therefore, if there be no first cause among efficient causes, there will be no ultimate, nor any intermediate cause. But if in efficient causes it is possible to go on to infinity, there will be no first efficient cause, neither will there be an ultimate effect, nor any intermediate efficient causes; all of which is plainly false. Therefore it is necessary to admit a first efficient cause, to which everyone gives the name of God.
The parent child example is a bit weak and not directly relevent to the point I think you are making. (To take away the cause is to take away the effect would be more generously exemplified by saying that to kill a man before he procreates is to kill his progeny. And that is quite reasonable an example of what Aquinas’s phrase may mean too).
Even the usual example given of what Aquinas meant (a locomotive jolting a train of tightly coupled carriages all the way to the rear caboose) is not instantaneous in the real world. All matter has some elasticity, even iron.
Also, like it or not, it seems time is intrinsic to the definition of sensible change and therefore of efficient causality even if it wasn’t what Aquinas was primarily saying. All worldly change, by definition, requires some duration of prior time to be associated with the instrumental causes. The word “change” may be problematic as below.
The problem I see here is that there is no consistency of definitions.
(a) While Aquinas is not really talking about time series that is clearly the sort of “sense world” examples he presents to the reader to start with. He even speaks about multiple efficient causes. But if he is not also talking about temporal time/causality why does he say this. For if he is really talking about ontological “sustaining” causality (causal series per se) then how can there be multiple efficient causes? There cannot. Only a god (who is existence) is capable of a “sustaining” efficient causality when we speak of being “per se”. Not even angels can assist there. So there can only be one such efficient cause anyway

. So its a case of I know what Aquinas meant but I heard what he said. Much analogy is at work in this 2nd Way.
(b) We only define/understand efficient causality by way of the senses. ie, by examples of temporal/material change. But the sort of efficient causality Aquinas really seems to be speaking of is about creation ex nihilo and “sustaining” of created things in existence. But we have no experience of such a “change” and strictly speaking we cannot assume this is an example of the same “change” or efficient causality as we know it. We cannot assume it works the same way. We can only speak by analogy not univocally.
Therefore logical defintions breakdown. It is especially hard to see how time is involved in such “change” or “efficient causality.”
I find it interesting that the Catholic Church never uses the word “change” when speaking of transubstantiation - presumably in acknowledgement of exactly the same limitation. We speak of “transforming” or passively “it will become for us…” - at least in the latin.