The Old Testament covers about 4000 years and God established the use of EXTERNAL rites right from the beginning used consistently between Genesis 3 to the introduction of the EXTERNAL rite of circumicsion with Abraham in Genesis 17:11. These EXTERNAL rites continued to Exodus 12 and the institution of the Passover under Moses and then a variety of EXTERNAL rites were added under the ceremonial law including the EXTERNAL rite of the Nazerine. The continuing use of EXTERNAL rites continued under the Mosaic law right to the book of Acts where Paul took the Nazerite vow in Jerusalem.
The design and intent of the EXTERNAL sacrificial rites has a consistency between Genesis and Acts. Jesus provides the intent in the healing of the leper in Luke 5:13-14:
13 And he put forth his hand, and touched him, saying, I will: be thou clean. And immediately the leprosy departed from him.
14 And he charged him to tell no man: but go, and shew thyself to the priest, and offer for thy cleansing, according as Moses commanded, for a testimony unto them.
A. When did the LITERAL cleansing occur? - v. 13 "immediately the leprosy departed from him"
B. Why was he told to shew himself to the Priest? - v. 14
1. "offer for thy cleansing"
2. "for a testimony unto them"
Now, was he sent to the preist IN ORDER that He might be LITERALLY cleansed of leprosy or to obtain FIGURATIVE ceremonial cleansing?
What was the design of this ceremonial cleansing? "For a TESTIMONY unto them".
Likewise, the writer of Hebrews and Colossians comments upon the literal versus figurative design and intent of external divine rites:
Heb. 10:1-4 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.
2 For then would they not have ceased to be offered? because that the worshippers once purged should have had no more conscience of sins.
3 But in those sacrifices there is a remembrance again made of sins every year.
4 For it is not possible that the blood of bulls and of goats should take away sins.
Col. 2:14 Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross;
15 And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it.
16 ¶ Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:
17 Which are a shadow of things to come; but the body is of Christ.
If you turn your back to the sun you can see YOUR shadow that is cast on the ground. Now, a truck can run over your shadow and not hurt you at all. However, if the truck ran over you it would hurt you. So your shadow is not you.
These EXTERNAL rites were as a "shadow" but the reality was Christ and his finished work. These "shadow" rites could NEVER LITERALLY REMOVE SIN but nevertheless the langauge of redemption was attached to them as they were commanded to offer up the sacrifices "for sin" and "for thy cleansing."
Literal remission of sins occurred in believing in the promised Christ of which these were all but Shadows:
"To him give ALL THE PROPHETS WITNESS that whosoever beleived in his name shall receive remission of sins" - Acts 10:43
Absolute proof that justification by faith (imputed righteousness and remission of sins - Rom. 4:6-8) occurred at the point of faith BEFORE submitting or offering such "shadow" type EXTERNAL ordinances is given in Romans 4:12 with Abraham as "THE FATHER OF ALL WHO BELIEVE" or the role model for all who are of faith.
Hence, the EXTERNAL rite whether sacrifices, circumcision, cleansing of the leper, nazerite vow, etc. were all "SHADOW" ordinances that remove sin FIGURATIVELY or CEREMONIALLY but NEVER LITERALLY.
Baptism is comparable to circumcision as an EXTERNAL rite just as the Lord's Supper is comparable to the passover as an EXTERNAL rite both of which are characterized by redemptive language that was attached to previous EXTERNAL rites "for the remission of sins" or "for sin."
God has not changed his design or intent for EXTERNAL divine rites as they only CEREMONIALLY cleanse beleivers from sins but NEVER LITERALLY REMOVE SIN as that is confusing the "shadow" with the "reality."
Hence, we should expect the same kind of redemptive language used with all other redemptive rites to be used with baptism and the Lord's Supper.
In Acts 2:38 "for remission of sins" is explained in keeping with the common language of all EXTERNAL redemptive ceremonial rites to be a "FIGURE" of what saves and remits sin, which is the death burial and resurrection of Jesus Christ - just as the Ark in Noah's day was a "LIKE FIGURE" of the death burial and resurrection of Jesus Christ "by water" as it lifted up the ark and all that were therein saving them from the flood. However, 100 years before the flood the Bible says "Noah found GRACE in the eyes of the Lord" just as 14 years before circumcision Abraham was already justified by faith, had imputed righteousness and remission of sins (Rom. 4:6-12).