With regard to the Chinaman who died 10 minutes after Baptism was instituted, firstly, some of the Fathers say that Baptism did not become obligatory for everyone until the Gospel had been preached throughout the world. Regardless, you forgot a very simple principle, that of God's PROVIDENCE. This man was not born into his condition by accident. Even today, I could have been born in the jungle amid a tribe of animists also, but for some reason, while God chose to put other souls there, he put me in a Catholic family. God has a reason for everything. If that soul was born a Chinaman right after the time of Our Lord, then God HAD A REASON for it. We don't know what it was. But things like that simply do not happen by accident. Perhaps he was born there because, had he known the Gospel and rejected it, he would have suffered a worse eternal fate, and the fact that he was born when and where he was, that was a mercy of God. If I die of a heart attack five minutes before I am scheduled to receive the Sacrament of Baptism, there was a REASON for that.
Most BoDers keep saying that God is not constrained by His Sacraments, and yet at the same time decide that God is constrained by circuмstances and accidents and impossibilities. That argument is utter nonsense. St. Augustine realized this and then backtracked from his initial support of BoD, referring this thinking as resulting in a "vortex of confusion".
St. Augustine:
If you wish to be a Catholic, do not venture to believe, to say, or to teach that 'they whom the Lord has predestinated for baptism can be snatched away from his predestination, or die before that has been accomplished in them which the Almighty has predestined.' There is in such a dogma more power than I can tell assigned to chances in opposition to the power of God, by the occurrence of which casualties that which He has predestinated is not permitted to come to pass. It is hardly necessary to spend time or earnest words in cautioning the man who takes up with this error against the absolute vortex of confusion into which it will absorb him, when I shall sufficiently meet the case if I briefly warn the prudent man who is ready to receive correction against the threatening mischief.
He is saying that if you think this way, you are not a Catholic. How many BoDers fit this description? And yet they pretend that St. Augustine is in "their corner" on the BoD issue. Nothing could be farther from the truth.
He came to this realization after battling the Pelagians and Donatists, and some of the strongest statements in existence AGAINST Baptism of Desire come from St. Augustine ... which even Karl Rahner realized.