And you shall offer a bull of a sin offering daily for atonement
And you shall offer a bull of a sin offering daily for atonement; and you shall purify the altar in your making atonement for it; and you shall anoint it to sanctify it. Exodus 29:36 KJ3

Forgiveness of sins before Jesus involved the killing of various animals not in the name of anybody. It took baptism to get a portion of the Jews to accept Jesus as the new name for forgiveness of sins. That is simply the 'faith of Jesus' that the Apostles speak of in Galatians 2:16.

Leviticus 16:29-34 ASV
(29) And it shall be a statute for ever unto you: in the seventh month, on the tenth day of the month, ye shall afflict your souls, and shall do no manner of work, the home-born, or the stranger that sojourneth among you:  (30)  for on this day shall atonement be made for you, to cleanse you; from all your sins shall ye be clean before Jehovah.  (31)  It is a sabbath of solemn rest unto you, and ye shall afflict your souls; it is a statute for ever.  (32)  And the priest, who shall be anointed and who shall be consecrated to be priest in his father's stead, shall make the atonement, and shall put on the linen garments, even the holy garments:  (33)  and he shall make atonement for the holy sanctuary; and he shall make atonement for the tent of meeting and for the altar; and he shall make atonement for the priests and for all the people of the assembly.  (34)  And this shall be an everlasting statute unto you, to make atonement for the children of Israel because of all their sins once in the year. And he did as Jehovah commanded Moses.

In Luke 16:30, we read that every year (not once and for all. Hebrews 10:1) the Jews start with a clean slate because it is written that 'for on this day shall atonement be made for you, to cleanse you; from all your sins shall ye be clean before Jehovah.' Note that verse 29 calls on them to afflict their souls to indicate that if someone did not afflict the soul that person would not benefit from the annual day of atonement. Jesus came to reveal to His people that He was the shadow of all the sacrificial works at the Temple and that He is the easier yoke to go with for remission of sins. Yet, as mentioned earlier, they rejected the enlightenment of the baptism of John which would have allowed them to recognize the Lamb.

To be honest, comparing today with the time of Jesus then, not all Jews would have welcomed the extraordinary new teaching of 'faith of Jesus', of which Jesus even spoke of the Jews to eat His flesh and drink His blood to be saved. We read that many disciples left following Him because of some of His crazy teachings like eating His flesh. So, when, today, as those disciples turned their back on Him, we reject any teaching of Jesus under any pretense, we also turn our backs to Jesus to follow instead other doctrines that itch our ears (Think, for an example, about the classical example of 3 days and 3 nights before Jesus was to be risen. We got Him to have risen in 2 days and 2 nights with 'solid' arguments to explain our myopia). In other words, keeping the observance of the day of atonement (Yom Kippur) is rejecting the atonement of Jesus from repentance and remission of sin in the faith of Jesus. Not to mention that our keeping of the festivals in Moses are not valid anyway because they require all the elements of the manners by which the feasts were to be conducted: the location, the Temple, the priesthood and the priests to do 'the works of the law'. 

(John 6:53 EMTV)
Then Jesus said to them, "Most assuredly, I say to you, unless you eat the flesh of the Son of Man and drink His blood, you have no life in yourselves.

(John 6:55 EMTV)
For My flesh truly is food, and My blood truly is drink.

John 6:66-69 EMTV

(66) From this time many of His disciples turned back and no longer would walk with Him.

(67) Then Jesus said to the twelve, "Do you also want to go away?"

(68) But Simon Peter answered Him, "Lord, to whom shall we go? You have the words of eternal life.

(69) Also we have come to believe and know that You are the Christ, the Son of the living God."

Romans3:21-31 summarizes the scope of the 'faith or belief in Jesus' Gospel (Acts 24:24) with Moses and the Prophets as the foundation of His Faith (Matthew 5:17).

Yom Kippur, for example is not a day to keep in the 'faith of Jesus' by the followers of Jesus if we want to truly abide in Him (John 15:10).

Purge out the old leaven, in order that you may be a new batch of dough, since you are unleavened. For indeed Christ, our Passover, was sacrificed for us. 1 Corinthians 5:7 EMTV