In Judaism there never was atonement for intentional sins through sacrifice. If you could atone through sacrifice for intentional sin than people would sin and feel all they had to do to atone was to make a sacrifice, no matter how horrible the sin. The only way to atone for an intentional sin, at all times in Judaism, including when the first and second Temple stood, was through prayer, repentance and charity. When the sin was against another person who was injured by the sin and incurred damage, then restitution was also required.
The Temple sacrifice was only for unintentional sins, did not necessarily require a blood sacrifice, for instance flour and incense were also used, and of course unintentional sin could also be atoned for by repentance, prayer and charity.
Christianity claims that Jews atoned for intentional sins through temple blood sacrifice. This is incorrect. Christian concepts concerning their messiah, of vicarious atonement, atonement through the sacrifice of human blood or atonement through faith rather than following the moral and ethical path of the Torah, all have no place in Judaism.
JL: Unintentional sin and Intentional sin, would be what the NT scripture and the Church call venial and mortal sin. 1Jn5:15 And if we know that he hear us, whatsoever we ask, we know that we have the petitions that we desired of him. 16 If any man see his brother sin a SIN which is NOT UNTO DEATH [venial not mortal], he shall ask, and he shall give him life for them that
SIN NOT UNTO DEATH [venial]. THERE IS A SIN UNTO DEATH [MORTAL]: I do not say that he shall pray for it. 17
All unrighteousness is sin: and
THERE IS A SIN NOT UNTO DEATH [venial].
I would be interested to see how you view the following OT scripture;
Lv 5:4 Or if a person thoughtlessly takes an oath to do anything, whether good or evil in any matter one might carelessly swear about even though he is unaware of it, in any case when he learns of it he will be guilty. 5 When anyone is guilty in any of these ways,
he must confess in what way he has sinned 6 and,
as a penalty for the sin he has committed, he must bring to the LORD a female lamb or goat from the flock as a sin offering; and the priest shall make atonement for him for his sin.
Lv 19:20-22 And whosoever lieth carnally with a woman, that is a bondmaid, betrothed to an husband, and not at all redeemed, nor freedom given her; she shall be scourged; they shall not be put to death, because she was not free. 21 And
he shall bring his trespass offering unto the LORD, unto the door of the tabernacle of the congregation, even a ram for a trespass offering. 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.
Nbs 5: 5-7 And the LORD spake unto Moses, saying, 6: Speak unto the children of Israel, When a man or woman shall commit any sin that men commit, to do a trespass against the LORD, and that person be guilty; 7:
Then they shall confess their sin which they have done: and he shall recompense his trespass with the principal thereof, and add unto it the fifth part thereof, and give it unto him against whom he hath trespassed.