The Catechism of the Catholic Church says some very succint things about baptism, but with regard to faith I can't seem to resolve this point. If I were to summarize, I'd say infants at the time of baptism neither have faith nor receive faith, exactly. Instead, they are cleansed from original sin and will develop faith when they are older and when they live in a Christian companionship: faith itself being a communal virtue and the individual participating in the faith of the Church.
In both of the above cases, faith is a supernatural gift: rooted in either an interior revelation or in an objective act of the Church.
The poet Charles Péguy says that faith is simple, that one would have to blind oneself not to have faith. Giussani says that faith is a basic dimension of human personality and that it's essential for society to exist. He also says that faith is acknowledging a presence. I seem to recall Thomas Aquinas saying that the value of faith is determined by its object. If so, this would mean that humans have a natural faith (best seen in the trust of an infant for its mother), but that when Jesus Christ is encountered in the face of the Church a new possibility arises for faith in the human person. It's not faith that changes, but the object. When Christ is encountered, faith in the person of Jesus Christ becomes possible. And this faith must grow through the person following Christ through the trials of life.
What do you think?