Where do you come up with these three things?
How can one have the faith "or the desire for them" when they've "never even heard of the existence of the sacrament of baptism?" Nobody desires that which they do not know exists. What you say is contrary to the catechism....

Where do I come up with those things?
It's from the Catechism, the very first book any serious Catholic should read. The two Catechisms traditionalists usually read are Trent's Catechism and St Pius X's catechism.
Which was recommended by St Pius X, as its name suggest, so His Holiness must have read it before approving it.