"But this man, after He had offered one sacrifice for sins forever, sat down on the right hand of God" (Hebrews 10:12).
Ever since Cain and Abel brought their offerings to the Lord in the first generation, and Noah "offered burnt offerings on the altar" after the Flood (Genesis 8:20), and then especially after God through Moses established the regular tabernacle offerings, including "the sin offering, and the burnt offering, and peace offerings" (Leviticus 9:22), it has somehow been understood everywhere that God (or "the gods" in pagan cultures) must be approached and appeased by sacrificial offerings, with innocent animals substituting for those offering them.
This was still true among Jewish worshippers of the true God even in Jesus' day, and they all understood that "without shedding of blood is no remission" (Hebrews 9:22). In those days, "every priest standeth daily ministering and offering oftentimes the same sacrifices, which can never take away sins" (Hebrews 10:11) just tentatively "cover" them.
But no more! Now, in personal faith, we need simply to "Behold the Lamb of God, which taketh away the sin of the world" (John 1:29). "For by one offering He hath perfected for ever them that are sanctified" (Hebrews 10:14). When we put our full trust in Him, "we are sanctified through the offering of the body of Jesus Christ once for all" and He has promised that "their sins and iniquities will I remember no more. . . . there is no more offering for sin" (Hebrews 10:10,17-18).
"So Christ was once offered to bear the sins of many; and unto them that look for Him shall He appear the second time without sin unto salvation. . . . For yet a little while, and He that shall come will come, and will not tarry" (Hebrews 9:28; 10:37). HMM