And, therefore, faith is the prior, most important, condition.
John came preaching "a baptism of repentance for the remission of sins."
The remission is from the "repentance" and not from the baptism. The baptism was the public proclamation of one's repentance.
When Peter spoke "repent and be baptized for the remission of sin" one's hermenutic should force one back to the verse that clarifies the sequence: "A baptism of 'repentance for the remission...'"
All sacraments are predicated on faith in their utility. And of course, you will agree that this faith is a gift entirely from God.
The remission is from the "repentance" and not from the baptism. The baptism was the public proclamation of one's repentance.
The Spirit came upon Christ during the Baptism - we use the same model and understanding. God acts through the visible sign, as He did through circumsion, or the Jews crossing through the Red Sea (at least that is how Peter saw it).
Yes, Baptism is for the forgiveness of sins. By being baptized, our sins are forgiven ("remissed").
Regards