Forgiveness is not a New Testament thing, ushered in by Jesus' death and resurrection. God has always made a way to obtain forgiveness. Hebrews 9:22 says "...without shedding of blood there is no forgiveness." From ancient times there has been a way to obtain forgiveness through the blood of animals, which represented the victims of sin. The priests made atonement by eating the flesh of the sacrifice, becoming one with the victim and then offering forgiveness representatively in the victim's place. Under the old covenant there was a way to be cleansed.
But Christ came to fulfill this Law. He established a second covenant which was better than the first. Christ's sacrifice did away with the need to offer the blood of animals year after year. His was not a temporary fix. Read Hebrews 9 &10.
Jesus said, "Eat my flesh". Of course he wasn't talking about cannibalism. He obviously had something else in mind. We are called to take part in His sufferings and follow His example. He willingly became the victim of our sin and offered a way of atonement. He calls us to do the same:
"For this finds favor, if for the sake of conscience toward God a person bears up under sorrows when suffering unjustly. For what credit is there if, when you sin and are harshly treated, you endure it with patience? [my note: This is obviously expected] But if when you do what is right and suffer for it you patiently endure it, this finds favor with God. For you have been called for this purpose, since Christ also suffered for you, leaving you an example to follow in His steps, who committed no sin, nor was any deceit found in his mouth; and while being reviled, He did not revile in return; while suffering, He uttered no threats, but kept entrusting Himself to Him who judges righteously; and He Himself bore our sins in His body on the cross, so that we might die to sin and live to righteousness; for by His wounds you were healed." 1 Peter 2:19 - 24
First there were animals, then Jesus, now us. God has given us a part in the evolution of the atonement process. The way to obtain forgiveness is to accept the gift of Jesus' sacrifice. The way not to loose it is to continue to forgive those who sin against us.
"For if you forgive others for their transgressions, your heavenly Father will also forgive you. But if you do not forgive others, then your Father will not forgive your transgressions."
The Day of Atonement is a day of fasting and humbling of souls (Leviticus 23:26-32). We can not enter into the Feast of Tabernacles without first going through the Day of Atonement.