This seems like a good opportunity to explain how the Catholic church really works. The Church teaches the doctrines that were passed down from the Apostles, nothing more, nothing less. That is why the Pope is infallible in areas of faith and morals - he doesn’t create new doctrine. Now to be fair, he does need to apply existing doctrine to new situations. For instance, artificial birth control was not available during apostolic times. when Pope Paul VI pronounced against the use of artificial birth control, he did so after prolonged prayer and study by a large group of bishops and he published the reasons that the ruling was an extension of existing doctrine.
As for the specific doctrine that God gives everone the opportunity to be saved, that is scriptural. After all, Jesus calls all men to himself. And to describe this practically, every one has a conscience to warn against evil and drive them toward good. That is God calling to every man to come to him, is it not?
as for Augustine: here is the support from the Catholic encyclopedia article on the teaching of Augustine:
But this decree includes also the second element of the Catholic dogma: the very sincere will of God to give to all men the power of saving themselves and the power of damning themselves. According to Augustine, God, in his creative decree, has expressly excluded every order of things in which grace would deprive man of his liberty, every situation in which man would not have the power to resist sin, and thus Augustine brushes aside that predestinationism which has been attributed to him. Listen to him speaking to the Manichæans: “All can be saved if they wish”; and in his “Retractations” (I, x), far from correcting this assertion, he confirms it emphatically: “It is true, entirely true, that all men can, if they wish.” But he always goes back to the providential preparation. In his sermons he says to all: “It depends on you to be elect” (In Ps. cxx, n. 11, etc.); “Who are the elect? You, if you wish it” (In Ps. lxxiii, n. 5). But, you will say, according to Augustine, the lists of the elect and reprobate are closed. Now if the non-elect can gain heaven, if all the elect can be lost, why should not some pass from one list to the other? You forget the celebrated explanation of Augustine: When God made His plan, He knew infallibly, before His choice, what would be the response of the wills of men to His graces. If, then, the lists are definitive, if no one will pass from one series to the other, it is not because anyone cannot (on the contrary, all can), it is because God knew with infallible knowledge that no one would wish to. Thus I cannot effect that God should destine me to another series of graces than that which He has fixed, but, with this grace, if I do not save myself it will not be because I am not able, but because I do not wish to