Sorry, I re-read your question. I think I was sleeping when I first read it, so let me try again, and with less technical language.
First of all, we need to understand the difference between essential and accidental cause, and the key idea for understanding that is
dependence.
If the effect would cease immediately when the cause ceases, then that effect depends
essentially (
per se) on its cause cause. Otherwise, no.
The problem with an infinite series of essential causes is that an infinite series has no beginning. There is nothing on which the effects can depend. Hence, the effects would not be produced.
If, however, the effect we are considering is only
accidentally dependent on its cause, there there is nothing preventing the effect from continuing on, even after the cause has gone out of existence.
We saw some examples: if I take cold iron, and place it in fire, the fire will change the iron from cold to hot. That change could not take place unless the iron were in the fire. Remove the iron from the fire, and heating immediately ceases: the effect (the change from cold to hot) depends
essentially on the fire.
On the other hand, remove the iron and, for a time, the iron will remain hot. What is the cause of the heat in the iron? In a way, it is the fire, but now the situation is slightly different: the heat in the glowing iron does not
depend on the fire. I could put the fire out, and the iron would stay hot (for a time). (If I could stop it from interacting with its environment somehow, it would stay hot indefinitely.) Hence, the heat depends now only
accidentally on the fire.
That is the difference. Whether it helps us in proving something about the temporal beginning of the universe, is a different matter.
Instantaneous action (Aquinas does not actually employ the expression “instantaneous motion”) would be an example of essential (
per se) cause. However, motion entails temporal succession, which includes a mix of both essential and accidental causes (similar to our iron example).
But is that part, at least, clear?
(Let’s tackle the problem of infinity once this part is cleared up.)