St. Thomas said flatly that God is not bound by the Sacraments.
It is not as though God could not do things another way, but He has chosen to reveal to us only that He has decided to do things in one specific way - the Sacramental system.
Yes, this is correct. I like you how phrased it: "he has chosen to reveal to us only that he has decided to do things in one specific way".
That does not preclude him from salvific action apart from the sacraments, but the certainty of such action is not revealed to us, therefore, we cannot trust in it if the sacraments are available.
Hence: Baptize your infants. Do not despair of the salvation of those who cannot be baptized through no fault of your own. Do not teach their salvation as an assured fact, either, however.
Of course God is bound by the Sacraments.
He has promised that every time one is properly celebrated, it will be effective.
Can God do things apart from the Sacraments? Yes, He is God, so he can do anything that is possible.
But should we expect Him to contradict Himself on the most grave issue of the salvation of mankind?
Faith comes by hearing, salvation by Baptism, eternal life from the Eucharist. God is needed for all three, but they can only come to a man by a man.
If there really was some other simple way for all those hordes of non-Christians so that they might be saved, why would God even bother with Catholicism and all its rituals and missions?
Isn't the fact that God does not just wave his hands, say abracadabra over us and make us saved tell us that it isn't some simple matter for God to save an infidel apart from the Church?
And isn't that because salvation is a cooperative effort on the part of God with the man being saved? And if that man is ignorant, base, wallowing in sins, apart from the communion of love in the Church, in short bereft of grace, what hope precisely are we to hold out to him other than the good news we should be preaching?
Yes, grace is pouring down constantly upon him, urging him to turnabout his life, but he has no sense of it because his spiritual eyes are closed, and he has no one to open them.
There he is, drowning in a sea of his own crimes that he cannot stop committing, and the modernist looks over at him from his perch atop a pile of divine life-preservers and says "Don't worry there old chap! You really aren't that bad a fellow after all! Don't you know that God will save you in the end regardless of what happens? It says it right here 'God will have all to be saved.' So stop that pitiful whimpering already, its disturbing my afternoon nap. I'd throw you one of these life preservers, but I would be greatly troubled by it because it would be patronizing to you to tell you you are drowning and can't be helped by your alternative religion. So just try to save yourself, okay? And in the mean time, quiet down."
Isn't the Catechism clear enough? "God wills the salvation of everyone through the knowledge of the truth." (No. 851). His universal will for salvation does not include willing the salvation of the ignorant in spite of themselves and their wilful resistance.
What is most disappointing is to think what if only the effort that had been used dreaming up specious reasoning to avoid missionary work had instead been put into being another St. Paul or St. Francis Xavier, especially amongst the clergy. For every St. Ignatius, 1000 of his sons are off in a corner scribling out new reasons to avoid the Great Commission.