"The Catholic belief is that original sin is removed through the grace of God at baptism, and holiness can be achieved through faith by grace."
I understand this to be, indeed, the belief of the Latin Church insofar as it relates to Baptism. It is of course not found among the Eastern Fathers. When did this belief first arise in the West? With +Augustine?
I don't know. My Catholic gut says it arose with "Do penance, and be baptized every one of you in the name of Jesus Christ, for the remission of your sins: and you shall receive the gift of the Holy Ghost". This sweeping "every one of you" suggests more than personal sin to be wiped clean with baptism. But I understand that you are looking for patristics.