CathInfo.com

Here’s the second aforementioned
resource:

• De Peccatorum Meritis et Remissione et de Baptismo Parvulorum

1.16.21 (CSEL 60, 20f.)


https://archive.org/details/corpusscriptorum60auguuoft/page/19/mode/1up?view=theater

I will post the third shortly.

Chapter 21 [XVI.]— Unbaptized Infants Damned, But Most Lightly; The Penalty of Adam's Sin, the Grace of His Body Lost.

It may therefore be correctly affirmed, that such infants as quit the body without being baptized will be involved in the mildest condemnation of all. That person, therefore, greatly deceives both himself and others, who teaches that they will not be involved in condemnation; whereas the apostle says: Judgment from one offense to condemnation, Romans 5:16 and again a little after: By the offense of one upon all persons to condemnation. Romans 5:18 When, indeed, Adam sinned by not obeying God, then his body — although it was a natural and mortal body — lost the grace whereby it used in every part of it to be obedient to the soul. Then there arose in men affections common to the brutes which are productive of shame, and which made man ashamed of his own nakedness. Genesis 3:10 Then also, by a certain disease which was conceived in men from a suddenly injected and pestilential corruption, it was brought about that they lost that stability of life in which they were created, and, by reason of the mutations which they experienced in the stages of life, issued at last in death. However many were the years they lived in their subsequent life, yet they began to die on the day when they received the law of death, because they kept verging towards old age. For that possesses not even a moment's stability, but glides away without intermission, which by constant change perceptibly advances to an end which does not produce perfection, but utter exhaustion. Thus, then, was fulfilled what God had spoken: In the day that you eat thereof, you shall surely die. Genesis 2:17 As a consequence, then, of this disobedience of the flesh and this law of sin and death, whoever is born of the flesh has need of spiritual regeneration — not only that he may reach the kingdom of God, but also that he may be freed from the damnation of sin. Hence men are on the one hand born in the flesh liable to sin and death from the first Adam, and on the other hand are born again in baptism associated with the righteousness and eternal life of the second Adam; even as it is written in the book of Ecclesiasticus: Of the woman came the beginning of sin, and through her we all die. Sirach 25:24 Now whether it be said of the woman or of Adam, both statements pertain to the first man; since (as we know) the woman is of the man, and the two are one flesh. Whence also it is written: And they two shall be one flesh; wherefore, the Lord says, they are no more two, but one flesh. Matthew 19:5-6

https://www.newadvent.org/fathers/15011.htm

While you're answering that, it seems my first argument was based on carelessly disregarding the context.

However, I haven't exhausted the quote. Here's the relevant part:

Notice two things:


1) Augustine says the punishment has an amount and kind which he does not know. Consider now that the deprivation of the Beatific Vision is a specific kind of punishment and which has no qualifier of amount. Therefore, Augustine is not speaking of merely their being in Hell. To restate the argument: if Augustine was claiming infants are only deprived of Heaven he wouldn't have said he cannot say what amount and kind of punishment they would suffer.

2) Augustine says: I dare not say it were better for them never to have existed than to exist there. Well, if Augustine held that the infants were in a state of perfect natural happiness, not suffering any positive punishment, then he would certainly say it was good for them to be born. However, he is not sure whether their punishment is of such a degree as to be better not to even exist.