The Old Testament sacrifices were counterparts of the reality, the Lord Jesus. They did not actually save the believer, only in type. It is not argued here that these sacrifices are analogous to Christian water baptism. So water baptism only saves the believer in type. The Old Testament Jew was saved before he brought the offering.
Water baptism is the outward testimony of the believer's inward faith.
The person is saved the moment he places his faith in the Lord Jesus. Water baptism is the visible testimony to his faith and the salvation he was given in answer to that faith. Baptism, Peter explains, does not wash away the filth of the flesh, either in a literal sense as a bath for the body, nor in a metaphorical sense as a cleansing for the soul. No ceremonies really affect the conscience. You will be his witness to all men of what you have seen and heard.