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.

As promised, here’s the third:

Contra Iulianum 5.11.44 (PL 44, 809).

I will post this one in English since I am aware of a faithful translation of it -

https://archive.org/details/fathersofthechur013910mbp

I hope the resources I posted help move this very important discussion forward in a positive direction.

It's not just any condemnation, but a damnatio cuм diabolo, condemnation or damnation with the devil, and it's a place of ignis aeternus, eternal fire.

I believe that "condemnation" you speak of (it wasn't in the Latin I looked at posted earlier), actually refers to poena, the actual suffering or affliction or torment part, and not just the condemnation.  But I'd have to find more of his Latin to be sure.

But it's important whether the "mildest" refers to the condemnation or the punishment.  These are potentially two distinct things.  Let's say that two of my children are involved in the same act of mischief.  I ground them both for 3 weeks.  So they get the same punishment.  But I know that the older one was exerting his influence over the younger one, so I am less upset with the younger one than with the older one.  Or, another analogy, two people cause $2,000 damage to my car.  One of them did so accidentally, the other vandalized the car out of spite.  Both owe me $2,000 in damages, and that would correspond to the poena, the penalty, but I'm not upset with the individual who did it accidentally, perhaps even feel sorry for him, but I'm angry at the one who did it deliberately.  So there's a distinction between guilt and punishment.

This distinction, BTW, is also the key to understanding Pope Pius IX's famous "invincible ignorance" passages, where he states that those not guilty of actual sin would not be afflicted with punishments, in Latin, the poenis, or penalties, but this does not necessarily mean they will be rewarded with Heaven.

St. Gregory nαzιanzen, in rejecting Baptism of Desire, states that there are some who are not bad enough to be punished but not good enough to be glorified.  Our Lord taught that those who believe and are baptized will be saved, but that those who do not believe will be condemned.  This leaves a middle ground of those who believe but are not baptized, where they fell into neither category.

But I do not say that children who die without the baptism of Christ will undergo such grievous punishment that it were better for them never to have been born, since our Lord did not say these words of any sinner you please, but only of the most base and ungodly. If we consider what He said about the Sodomites, which certainly He did not mean of them only that it will be more tolerable for one than for another in the day of judgment, 2 who can doubt that nonbaptized infants, having only original sin and no burden of personal sins, will suffer the lightest condemnation of all? I cannot define the amount and kind of their punishment, but I dare not say it were better for them never to have existed than to exist there. But you, also, who contend they are, as it were, free of any condemnation, do not wish to think about the condemnation by which you punish them by estranging from the life of God and from the kingdom of God so many images of God, and by separating them from the pious parents you so eloquently urge to procreate them. They suffer these separations unjustly, if they have no sin at all; or if justly, then they have original sin.


The Fathers Of The Church A New Translation Volume 35 Saint Augustine Against Julian : Roy Joseph Deferrari : Free Download, Borrow, and Streaming : Internet Archive

I am myself keenly aware of how profoundly problematic this question is, and I recognize that my powers are not sufficient to get to the bottom of it. Here too I like to exclaim with Paul, Oh the depths of the riches! (Rom 11:33). Unbaptized babies go to damnation; they are the apostle's words, after all: From one to condemnation (Rom 5:16).8 I cannot find a satisfactory and worthy explanation-because I can't find one, not because there isn't one. So where, in the depths, I cannot find bottom, I must take account of human weakness, not condemn divine authority. I certainly exclaim, and I'm not in the least ashamed of it, Oh the depths of the riches of the wisdom and knowledge of God! How inscrutable are his judgments, and untraceable his ways! For who has come to know the mind of the Lord, or who has been his counselor? Or who first gave to him, and will be repaid? Because from him, and through him, and in him are all things; to him be glory for ever and ever (Rom 11:33-36).