That nothing happens without God we know from many sources; and, reversely, that God's dispensations have no element of chance and confusion in them every one will allow, who realizes that God is Reason, and Wisdom, and Perfect Goodness, and Truth, and could not admit of that which is not good and not consistent with His Truth. Whether, then, the early deaths of infants are to be attributed to the aforesaid causes, or whether there is some further cause of them beyond these, it befits us to acknowledge that these things happen for the best.
I have another reason also to give which I have learned from the wisdom of an Apostle; a reason, that is, why some of those who have been distinguished for their wickedness have been suffered to live on in their self-chosen course. Having expanded a thought of this kind at some length in his argument to the Romans, and having retorted upon himself with the counter-conclusion, which thence necessarily follows, that the sinner could no longer be justly blamed, if his sinning is a dispensation of God, and that he would not have existed at all, if it had been contrary to the wishes of Him Who has the world in His power, the Apostle meets this conclusion and solves this counter-plea by means of a still deeper view of things.
He tells us that God, in rendering to every one his due, sometimes even grants a scope to wickedness for good in the end. Therefore He allowed the King of Egypt, for example, to be born and to grow up such as he was; the intention was that Israel, that great nation exceeding all calculation by numbers, might be instructed by his disaster. God's omnipotence is to be recognized in every direction; it has strength to bless the deserving; it is not inadequate to the punishment of wickedness; and so, as the complete removal of that peculiar people out of Egypt was necessary in order to prevent their receiving any infection from the sins of Egypt in a misguided way of living, therefore that God-defying and infamous Pharaoh rose and reached his maturity in the lifetime of the very people who were to be benefited, so that Israel might acquire a just knowledge of the two-fold energy of God, working as it did in either direction; the more beneficent they learned in their own persons, the sterner by seeing it exercised upon those who were being scourged for their wickedness; for in His consummate wisdom God can mould even evil into co-operation with good. The artisan (if the Apostle's argument may be confirmed by any words of ours)— the artisan who by his skill has to fashion iron to some instrument for daily use, has need not only of that which owing to its natural ductility lends itself to his art, but, be the iron never so hard, be it never so difficult to soften it in the fire, be it even impossible owing to its adamantine resistance to mould it into any useful implement, his art requires the co-operation even of this; he will use it for an anvil, upon which the soft workable iron may be beaten and formed into something useful. But some one will say, “It is not all who thus reap in this life the fruits of their wickedness, any more than all those whose lives have been virtuous profit while living by their virtuous endeavours; what then, I ask, is the advantage of their existence in the case of these who live to the end unpunished?” I will bring forward to meet this question of yours a reason which transcends all human arguments. Somewhere in his utterances the great David declares that some portion of the blessedness of the virtuous will consist in this; in contemplating side by side with their own felicity the perdition of the reprobate. He says, “The righteous shall rejoice when he sees the vengeance; he shall wash his hands in the blood of the ungodly”; not indeed as rejoicing over the torments of those sufferers, but as then most completely realizing the extent of the well-earned rewards of virtue. He signifies by those words that it will be an addition to the felicity of the virtuous and an intensification of it, to have its contrary set against it. In saying that “he washes his hands in the blood of the ungodly” he would convey the thought that “the cleanness of his own acting in life is plainly declared in the perdition of the ungodly.” For the expression “wash” represents the idea of cleanness; but no one is washed, but is rather defiled, in blood; whereby it is clear that it is a comparison with the harsher forms of punishment that puts in a clearer light the blessedness of virtue. We must now summarize our argument, in order that the thoughts which we have expanded may be more easily retained in the memory. The premature deaths of infants have nothing in them to suggest the thought that one who so terminates his life is subject to some grievous misfortune, any more than they are to be put on a level with the deaths of those who have purified themselves in this life by every kind of virtue; the more far-seeing Providence of God curtails the immensity of sins in the case of those whose lives are going to be so evil. That some of the wicked have lived on does not upset this reason which we have rendered; for the evil was in their case hindered in kindness to their parents; whereas, in the case of those whose parents have never imparted to them any power of calling upon God, such a form of the Divine kindness, which accompanies such a power, is not transmitted to their own children; otherwise the infant now prevented by death from growing up wicked would have exhibited a far more desperate wickedness than the most notorious sinners, seeing that it would have been unhindered. Even granting that some have climbed to the topmost pinnacle of crime, the Apostolic view supplies a comforting answer to the question; for He Who does everything with Wisdom knows how to effect by means of evil some good. Still further, if some occupy a pre-eminence in crime, and yet for all that have never been a metal, to use our former illustration, that God's skill has used for any good, this is a case which constitutes an addition to the happiness of the good, as the Prophet's words suggest; it may be reckoned as not a slight element in that happiness, nor, on the other hand, as one unworthy of God's providing.
Source: On Infants' Early Deaths (New Advent)