The sacrificial system was put in place so the people's sins could be forgiven. If a Jew died in his sin, they were cut off from God for eternity. I can post many, many more if needed.
Sins could be forgiven under the law, but not washed away.
Leviticus 4:20
And he shall do with the bullock as he did with the bullock for a sin offering, so shall he do with this: and the priest shall make an atonement for them, and it shall be
forgiven them.
Leviticus 4:26
And he shall burn all his fat upon the altar, as the fat of the sacrifice of peace offerings: and the priest shall make an atonement for him as concerning his sin, and it shall be
forgiven him.
Leviticus 4:31
And he shall take away all the fat thereof, as the fat is taken away from off the sacrifice of peace offerings; and the priest shall burn it upon the altar for a sweet savour unto the Lord; and the priest shall make an atonement for him, and it shall be
forgiven him.
Leviticus 4:35
And he shall take away all the fat thereof, as the fat of the lamb is taken away from the sacrifice of the peace offerings; and the priest shall burn them upon the altar, according to the offerings made by fire unto the Lord: and the priest shall make an atonement for his sin that he hath committed, and it shall be
forgiven him.
Leviticus 5:10
And he shall offer the second for a burnt offering, according to the manner: and the priest shall make an atonement for him for his sin which he hath sinned, and it shall be
forgiven him.
Leviticus 5:13
And the priest shall make an atonement for him as touching his sin that he hath sinned in one of these, and it shall be
forgiven him: and the remnant shall be the priest's, as a meat offering.
Leviticus 5:16
And he shall make amends for the harm that he hath done in the holy thing, and shall add the fifth part thereto, and give it unto the priest: and the priest shall make an atonement for him with the ram of the trespass offering, and it shall be
forgiven him.
Leviticus 5:18
And he shall bring a ram without blemish out of the flock, with thy estimation, for a trespass offering, unto the priest: and the priest shall make an atonement for him concerning his ignorance wherein he erred and wist it not, and it shall be
forgiven him.
Leviticus 6:7
And the priest shall make an atonement for him before the Lord: and it shall be
forgiven him for any thing of all that he hath done in trespassing therein.
Leviticus 19:22
And the priest shall make an atonement for him with the ram of the trespass offering before the Lord for his sin which he hath done: and the sin which he hath done shall be
forgiven him.