And Your purposes were profoundly impressed upon me; and, rejoicing in faith, I praised Your name. And that faith suffered me not to be at rest in regard to my past sins, which were not yet forgiven me by Your baptism. [Confessions, IX.4]
We see here that St. Augustine considered himself already to have faith, but he knew that this would not save. His sins had to be forgiven, and this, he knew, must be done in Baptism.
We see the same thing in chapter 6 of the same book of the Confessions, where he writes concerning his son and others who were baptized at the same time as he:
Quickly did You remove his life [i.e., that of St. Augustine’s son Adeodatus] from the earth; and now I recall him to mind with a sense of security, in that I fear nothing for his childhood or youth, or for his whole self. We took him coeval with us in Your grace, to be educated in Your discipline; and we were baptized, and solicitude about our past life left us. [ibid., IX.6]
Why was he no longer worried about his past life? Because his sins were forgiven in baptism. Faith didn’t do this, as the first quotation above makes clear; it was the sacrament.