The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[Bucky Ball]

Lol, I just quoted the Catechism. I obviously don't deny its Truth. Yes, Baptism of Desire exists, and Baptism of Desire, as St. Thomas explains, means an act of faith in Christ, and an act of contrition for our sins. St. Thomas also explains the one saved by Baptism of Desire will go to Purgatory. It has some of the effects of Sacramental Baptism but not all. Sacramental Baptism takes a soul to Heaven even without Purgatory, provided he dies shortly thereafter without committing any sin. Bottom line: those who have heard of Christ at least are bound to accept Him as Lord and Savior, and be contrite for their former sins.

Christ said: "Unless a man be born again of Water and the Holy Spirit, he cannot enter the Kingdom of God" (John 3:5)

In these words, He sufficiently taught that once we know Baptism to be necessary, we must receive this Re-Birth/Regeneration in Water and in Spirit, to enter the Kingdom of God. This is what also all the Church's Missionaries like St. Francis Xavier and St. Patrick, the Apostle of Ireland, knew very well.

That's just the problem. You can't assume they "know (or believe) that Baptism is necessary". 
There is NOTHING in Roman Theology as taught today that says "It has some of the effects of Sacramental Baptism but not all."
You're denying you church's teaching.