In http://www.thesumma.info/one/one29.php , Fr Reginald Garrigou-Lagrange (GL) writes about the principle of causality, or more precisely the principle of efficient causality:
As a matter of fact, this principle is commonly formulated not only in the phenomenal but also in the ontological order, and not only does it state that "every phenomenon supposes an antecedent phenomenon," but it also says: "Everything that comes into being has a cause"; or rather, to express it more universally, every contingent being is efficiently caused by another. Even if de facto this contingent being eternally existed, it would still need a productive and conservative cause, because a contingent being is not its own reason for existence.
Comparing it with the modal cosmological argument, or argument from contingency, as stated by Prof. Edward Feser in:
What defenders of the cosmological argument do say is that what comes into existence has a cause, or that what is contingent has a cause.
it is clear that the modal cosmological argument as stated by Prof. Feser is identical to the principle of efficient causality as stated by Fr GL. This is confirmed by another text from Fr GL at:
The principle of efficient causality also finds its formula as a function of being. Wrong is the formula: "Every phenomenon presupposes an antecedent phenomenon." The right formula runs thus: "Every contingent being, even if it exists without beginning,  needs an efficient cause and, in last analysis, an uncreated cause."
Back to the first link from Fr GL, he attempts to show that "one cannot deny the principle of causality without denying the principle of contradiction."
First he argues that "uncaused contingent being is repugnant to reason. In other words, nothing is what results from nothing, without a cause nothing comes into being." However, the second statement, while obviously true, does not prove the first, because an uncaused contingent being does not NEED to have "come into being", it could just have always existed. (To accommodate current science, that would be a hypothetical "metaverse" undergoing eternal inflation, in which "pocket universes" such as ours would pop up here and there.) That would mean that such a being would be a brute fact and not explainable by reason, which is not the same as "repugnant to reason". In other words, that possibility would be against the Principle of Sufficient Reason (PSR) but not against the principle of (non-)contradiction (PNC) as Fr GL argues.
Fr GL repeats his argument in the same paragraph:
Why is an uncaused contingent being repugnant to reason? It is because a contingent being is that which can either exist or not exist (this being its definition). Therefore it is not self-existent, and must be dependent upon another for this; otherwise, if it were neither self-existent nor dependent upon another for existence, it would have no reason for existing, and so would be the same as nothing. "Nothing is what results from nothing." To say that from nothing, or that from no cause either efficient or material, something comes into being, is a contradiction.
IMV, there are three non-sequiturs in this paragraph.
First, that a being "can either exist or not exist" means that it does not have in itself the reason for its existence. However, that does not imply that "it is not self-existent", but rather that "it is not self-existent IF reality is rationally explainable". Therefore, a contingent being can be either a self-existent brute fact, if reality is not rationally intelligible, or dependent upon another for its existence, if reality is rationally intelligible.
Second, Fr GL is right when he says that if a contingent being "were neither (rationally intelligibly, I add) self-existent nor dependent upon another for existence, it would have no reason for existing". However, that does not entail that such a contingent being "would be the same as nothing". Because to "have no reason for existing", to be a brute fact, is not the same as to "be the same as nothing". Not being rationally explainable is not the same as not being.
Third, Fr GL is right when he says that: ""Nothing is what results from nothing." To say that from nothing, or that from no cause either efficient or material, something comes into being, is a contradiction." However, a contingent universe (or metaverse) could just have always existed without having ever come into being, so that its existence, while being a brute fact and as such against the PSR, would not imply a contradiction.
Summarizing, then, a contingent being is that which can either exist or not exist (by definition), so that, when referring to the universe (or metaverse), there are three posibilities:
a. it is dependent upon the Subsistent Being for its existence, (in which case both the PNC and the PSR hold),
b. it exists by itself, and has always existed, as a non-rationally intelligible brute fact, (in which case the PNC holds but the PSR does not),
c. it has come into being from nothing, as a brute fact repugnant to reason, (in which case neither the PNC nor the PSR holds).
From this, two conclusions:
First, as the modal cosmological argument, or argument from contingency, is just the principle of efficient causality, it is based on just the PSR  and does not require the aristotelical framework of act and potency. This is an important result, because otherwise St Paul's statement that "since the creation of the world God's invisible attributes, his eternal power and divine nature, are clearly seen, being understood through the things that are made" (Rom 1:20) would need to be restated as "since Aristotle wrote his Metaphysics God's invisible attributes, his eternal power and divine nature, are clearly seen, being understood through the things that are made".
Second, it seems that the teaching in First Vatican Council's Constitution Dei Filius "that God, the beginning and end of all things, can be known with certainty by the natural light of human reason from created things;" as well as the above Pauline statement that Dei Filius quotes right next as basis for that teaching, presupposes the implicit condition "if the person in question assumes that reality is ultimately intelligible/explainable by human reason". 
Thus, the issue of theism vs atheism (agnosticism) would not be really philosophical but meta-philosophical, as the latter positions would be based on the assumption that reality as a whole is not (necessarily) rationally intelligible/explainable.
Which is exactly David Hume's position as summarized by Texas A&M University Prof. of Philosophy Stephen H. Daniel :
"The argument assumes that the world's existence can be explained rationally by appeal to God as its cause; but why should we think that the world's existence is rationally explainable?"
And which is the basis of the "Thesis 1" that I propose on the next article.
 That PSR is sufficient for PC was confirmed by Prof. Edward Feser in an article he published in his blog on 2014 09 06:
a Scholastic might (as some Neo-Scholastic writers did) argue for PC on the basis of the principle of sufficient reason (PSR).
[I]f PC were false — if the actualization of a potency, the existence of a contingent thing, or something’s changing or coming into being could lack a cause — then these phenomena would not be intelligible, would lack a sufficient reason or adequate explanation. Hence if PSR is true, PC must be true.
 That PSR is necessary for PC was confirmed by Prof. Edward Feser in an article he published in his blog on 2014 11 02:
"Now if PSR is false, then the principle of causality is threatened as well, since if things are ultimately unintelligible, there is no reason to think that a potency might not be actualized even though there is nothing actual to actualize it and thus that something contingent, like the universe, might just be without any cause at all. But then it would not be possible to argue from the world to God as cause of the world."
 Test Questions for Phil 251: Intro. to Philosophy, Philosophy of Religion, option 101.B
(where options 99 and 101 should say "cosmological", not "teleological", argument).