From what I’ve read it seems that at least the first two categories of people would not have posed a problem to the conscience of the earliest Christians – because the earliest Christians did not believe in original sin and inherited guilt. Rather they believed that we are born innocent. However, we are born into a world of death and into solidarity with humanity that is oriented towards death because of the first sin of Adam. And this leads us eventually into sin – but not in the earliest years of infancy
For example Origen viewed children as being born completely innocent, He gave reasons for this. For one thing – he argued - children behave the same way to rich and powerful people as they do to poor and inconsequential people. So they are not affected by pride and power.
But Origen also believed in the innocence of children because he did not read inherited guilt into Paul’s theology. Augustine was the first to really do this and, in doing so created the problem of the unbaptized – the aborted, the stillborn, the ones who die very early before baptism – whom he consigned to eternal torment on the grounds of their possessing inherited guilt that has not been sacramentally cleansed and therefore being creatures of God’s wrath.
Gregory of Nyssa, by way of contrast, in his pastoral letter ‘On Infants’ Early Deaths’, addressed the issue from an Origenian position. The deaths of infants did not present him with any need to think about the prospect and justice of their eternal damnation – because Gregory was a universalist and also had no concept of ‘inherited guilt s’. And in similar vein, the crux of the matter for him was not that unbaptized infants who die prematurely had no opportunity to be saved, but rather that they’d had not opportunity in this life to develop towards their goal/‘telos’ (which is, as with the rest of us, growing from the image of God into the likeness of God). Gregory concluded that God will give them these opportunities in post mortem existence.
Regarding the question of why some infants die young, Gregory speculates rather tortuously that perhaps God foreknows that these children would grow up to live especially wicked lives. But he ends by adding, rather more helpfully:
“But seeing that our reason in this matter has to grope in the dark, clearly no one can complain if its conjecturing leads our mind to a variety of conclusions.