The general structure of the argument is: All equivocal agent causes are analogously named with their effects; God is an equivocal agent cause, therefore he is named analogously with his effects. The first step here is to consider God as an agent cause.
The first consideration of God as an efficient cause in the Summa Theologicae is in the second proof for God’s existence. The argument in brief is that if there were no first efficient cause, then in any order of efficient causes, all causes would be intermediate or secondary. But to be secondary is only possible in relation to some first, so some first agent cause exists, and this is what all call God.
Perhaps the first and easiest objection to the proof is that it seems simply false on its face: we experience all kinds of first efficient causes that we would never think to call God. If I hit a golf ball, there is certainly an order of efficient causality there, but why do I need to trace it back to any agent other than myself?
Note carefully that St. Thomas is not speaking about “a first cause in some qualified sense” or “the first cause in this or that order of causality (which is the same thing)”, but the first efficient cause simply. It’s true that I am the first efficient cause if one stipulates that they are talking about me hitting this golf ball, but it does not follow from this that one calls me “the first efficient cause” simply. Considered in relation to my parents (in my moment of generation), I’m not a cause at all, but an effect. St. Thomas is not talking about a first efficient cause in a qualified sense, for the simple reason that one does not necessary to prove that there is such a cause- so far as one is concerned with only qualified first causes it is sometimes possible simply to stipulate them.
I might also point out that we are effects of agent causes in far more profound ways than we tend to recognize. Whatever property is responsible for holding all the parts of my body together is very much an agent cause of my existence: water, for example, has no such force. If one could simply shut this force off with the turn of a key, I immediately collapse and dissipate (someday, of course, this force will gradually cease to act).
The second way does not come to rest in some cause like myself, or for that matter in anything, no matter what it is, that is in some way an effect- even an effect of the property that holds its parts together. This is necessarily a cause above physical, material existence, and in this sense beyond nature. This is why St. Thomas can say with confidence that it is “what all call God”.