"One of the most contested aspects of Lutheran theology when talking to people tends to be the concept that infants have faith. Luther vigorously upheld the ancient practice of infant baptism against the anabaptist movement, and also sought to uphold baptismal efficacy. An objection which he often encountered was that since salvation is by faith alone, how can baptism save an infant, who does not yet have faith? Rather than answering the question in the way that Augustine does, wherein a parent's faith or the church's faith is imputed to the child, Luther argued that infants do indeed have faith.
In opposition to what human reason might suppose, infants can have faith. The Biblical testimony on this is clear. Look for example at Psalm 22.
"Yet you are he who took me from the womb;
you made me trust you at my mother's breasts.
On you was I cast from my birth,
and from my mother's womb you have been my God." (Psalm 22:9-10)
In this Psalm, David discusses his faith, and in doing so references the fact that he had faith at a time when he was still nursing. How is this possible? The answer is just as clear, "you made me trust you." In Reformation theology (and all Augustinian theology for that matter)faith is a gift of God. It is not a human achievement, not something that one chooses out of a free will. If this were so, then infant faith would be impossible. But according to a monergistic scheme, faith is a divine gift, a divine work through the operation of the Holy Spirit. This being the case, why is it not possible that God could do such a work for an infant? To argue otherwise seems to imply that there is something necessary in a person for faith to be a possibility. This is in opposition to Reformation theology.
Peter Leithart makes the argument that infant faith is proven by the fact that we talk to infants. If we spend time talking to infants, and interacting with them, we do so because we know that they have an awareness of others. However limited that awareness might be, it is apparent. Are we, as Christians, willing to say that this is the case with other human beings but not God? Is not the reality of God even more apparent and real than that of creation? An infant has to constantly look outside of themselves to receive help; they look to others to get food, to move to where they need to be,and for every type of sustenance in life. Is this not precisely what faith is? Looking to one outside of ourselves as helpless creatures?"
For more, check out Jordan Cooper's blog: Just and Sinner.
Here's another article on awareness in newborns.