When we think about how causality works in Thomas' arguments the temptation is to think of causality univocally. That is to say, we are tempted to think of God's "causality" as being similar to creaturely causality. In this imagination, which is hard to escape, God is a cause among or alongside other causes. Perhaps the "first cause," but a cause like all other causes.
The problem here is that what makes God's "causality" different isn't its being "first," its temporal primacy. Rather, God's "causality" is wholly different from any understanding we might have of causality. When we say God "causes" something we have no idea what that might mean. Which is why I've been putting "causality" in scare quotes when applied to God.
In the Summa, Thomas gets at this distinction by making a contrast between primary (God) and secondary (creaturely) causality. And by "primary" Thomas doesn't just mean "temporally prior to." He also means "ontologically different."
Now, people have long puzzled over how primary causality relates to secondary causality. Some even find the relationship incoherent. The "causal joint" between divine and creaturely causality is hard to specify. I don't want to deny those puzzles and questions. I simply want to note that the mysteries here are due to the fact that we can't conceive of how God is a "cause." There is an apophatic mystery on one side of the equation which means any "mechanistic" understanding of the divine/creaturely relationship will always be epistemically thwarted. We just can't imagine how God's "causality" is working on His side of the relationship.
The simple point here is that when we think about Thomas' arguments for the existence of God, especially his arguments about infinite causal regress, we should never imagine a chain of dominos falling, where God is the first domino. God isn't a domino among other dominos. Whatever God does as "first cause" or "primary cause," as both Creator and Sustainer, is unlike anything we can imagine. God "causes" differently. And because of that, an apophatic Mystery haunts all of Thomas' arguments for the existence of God. So while Thomas' arguments seem to be logical proofs, they are actually the first step toward a mystical encounter with God.