Aaron’s offering the sin offering and the burnt offering to make expiation for himself first (v. 7) signifies that he, as a sinful person, needed to take Christ as his sin offering and burnt offering so that his situation with God might be appeased and he might serve God as a priest. See note Lev. 8:141 and note Lev. 8:181.
Aaron’s preparing the sin offering and the burnt offering also typifies Christ’s offering Himself as a sin offering for the redemption of God’s people and as a burnt offering for God’s people to be God’s satisfaction (Heb. 9:14; 10:5-10). Moreover, it signifies that whatever Christ as our High Priest did, He did for us, that we might be redeemed from sin and made God’s satisfaction. By our being one with Christ in His death, we are redeemed in Him (Eph. 1:7), and by Christ’s being one with us in His resurrection, He lives in us that we may live Him for God’s satisfaction (Gal. 2:20; Phil. 1:20-21a).