How did the Canaanite woman come to believe? We don’t know exactly. The text does not say. But what we DO know however is that the ultimate answer to the question of how this woman came to know and believe is that the Lord revealed it to her. She is, like the Magi and the centurion before her; and like you and I; an unlikely candidate for such faith. That, however, is the way of God, to hide things from the wise and scholarly and noble, and instead to reveals these things to infants.
-Aj Neugebauer LCMS pastor