The Westminster Confession chapter 7 paragraph 5 says this
V. This covenant was differently administered in the time of the law, and in the time of the gospel: under the law, it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all fore-signifying Christ to come: which were, for that time, sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation; and is called, the Old Testament.
2 Cor. iii. 6, 7, 8, 9; Heb. viii., ix., x. chapters; Rom. iv. 11; Col. ii. 11, 12; 1 Cor. v. 7; 1 Cor. x. 1, 2, 3, 4; Heb. xi. 13; John viii. 56; Gal. iii. 7, 8, 9, 14.
The term forgiveness is used copiously in the Old Testament. David may even sing about it from personal experience "Blessed is he whose trasngression is forgiven, whose sin is covered". (Psalm 32.1). See Paul's interpretation of this in Romans 4.6-8 "Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works, Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.Blessed is the man to whom the Lord will not impute sin."
The sacrifices were not efficacious of themselves to take away sin, but were means by which the coming sacrifice of Christ was applied to the Old Testament saints who participated in them by faith. In both OT and NT it is the work of Christ alone that is the grounds for forgiveness.
Reformed Presbyterian Church