I believe the following type-antitype chart will help you to understand the correlation between animal sacrifices and how they represented Christ.
|Leviticus 4:3, 23, 28. The animal was to be without blemish.||1 Peter 1:19. Christ was “without blemish and without spot.”|
|Leviticus 4:4, 14. The offering was to be brought before the Lord to the door of the sanctuary.||Hebrews 4:15, 16. “Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.”|
|Leviticus 4:4; Numbers 5:7. The sinner laid his hand on the head of the offering, thus acknowledging his sins.||1 John 1:9. “If we confess our sins, He is faithful and just to forgive us our sins.”|
|Leviticus 4:29. The sinner slew the sin-offering; he took the life of the lamb with his own hands.||Isaiah 53:10. Christ’s soul was made an offering for sin. Criminals often lived for days upon the cross; it was the awful burden of the sins of the world that slew Christ.|
|Leviticus 4:5–7, 17, 18. In some offerings the blood was taken into the sanctuary and sprinkled before the Lord.||Hebrews 9:12. “By His own blood He [Christ] entered in once into the holy place, having obtained eternal redemption for us.”|
|Leviticus 10:16–18. When the blood was not taken into the sanctuary, a portion of the flesh was eaten by the priest in the holy place; thus in type the priest bore “the iniquity of the congregation to make atonement for them before the Lord.”||1 Peter 2:24. This was a type of the One “Who His own self bare our sins in His own body on the tree, that we, being dead to sins, should live unto righteousness: by whose stripes ye were healed.”|
|Leviticus 4:31; 7:30. The sinner with his own hands was to separate all the fat from the sin-offering, the fat typifying sin. Psalm 37:20.||Isaiah 1:16. We are not only to confess past sins, but we are to examine our own hearts and put away evil habits. “Cease to do evil.”|
|Leviticus 4:31. The fat is all burned to ashes in the court of the sanctuary.||Malachi 4:1–3. All sin and sinners will be burned to ashes on the earth.|
|Leviticus 4:7, 18, 25, 30. The blood of every sin-offering was poured on the ground at the bottom of the brazen altar in the court.||Ephesians 1:14. Christ purchased the earth as well as its inhabitants by His death on the cross.|
The Cross and Its Shadow, by Stephen N. Haskell, reprint by The Review and Herald Publishing Company, 130, 131.