Yes, a Catholic can be a young Earth creationist in good faith
1. The question of the origin of man’s body from pre- existing and living matter is a legitimate matter of inquiry for natural science. Catholics are free to form their own opinions, but they should do so cautiously; they should not confuse fact with conjecture, and they should respect the Church’s right to define matters touching on Revelation.
2. Catholics must believe, however, that the human soul was created immediately by God. Since the soul is a spiritual substance it is not brought into being through transformation of matter, but directly by God, whence the special uniqueness of each person.
[Richard Dawkins has picked up on this and denounced the Church for it, revealing how little true meeting of minds there could ever between Catholicism and Darwinism.]
3. All men have descended from an individual, Adam, who has transmitted original sin to all mankind. Catholics may not, therefore, believe in “polygenism,” the scientific hypothesis that mankind descended from a group of original humans.