Growing numbers of Christians no longer believe in original sin. Paul used the sacrifice of Jesus simply as a tool to get people off of the Mosaic law.
If if you're a child afraid of the boogeyman in the closet and I set up a teddy bear next to the closet saying, "don't worry, teddy will protect you", the bear is just a tool to get the child's focus off his fear. But the bear has no real power.
Similarly, Jesus' sacrifice was simply a talking point to tell people, "see! You don't have to follow all these laws and sacrifices anymore. Jesus was your sacrifice once and for all".
Jesus never taught forgiveness of sins through sacrifice. He taught forgiveness of sins to the extent that you forgive others. There is no concept of inherited or original sin in the Hebrew Scriptures. That is a later Christian development.