So then why is the Church's official position that they don't know what the fate of an unbaptized infant would be?
The Church doesn't know everything, especially the fate of souls after death. It is true that the Church has canonized a small percent of people and declared that the person is in Heaven, but the Church doesn't declare for certain that anyone is in Hell. Hell could be empty. The Church doesn't know whether there is a single person there.
The Church is simply admitting she doesn't know one way or the other. The Magisteriium admits that there is a limit to it's understanding.
The Church has also never taught that they do go to Heaven.
Yes, because they were not baptized, the Church simply has a mystery it doesn't know how to solve. Sort of like, when a person dies in what the Church defines as mortal sin, the Church doesn't declare that we can know the person is damned.
Mortal sin is defined and then is at the same time a gray matter. Many people who commit mortal sin are not in a state of mortal sin, because of habits, mental health issues, and ignorance.
The Catechism says that the soul in mortal sin has turned it's back on God and charity is destroyed in their heart. However, many people that commit these "mortal sins" haven't turned their back on God and still have charity.
So the Church simply doesn't know what their fate is.