What did God do with the sins of Old Testament believers before Christ died?
Before Christ's death, God did not remove Old Testament believers' sins through the Day of Atonement sacrifices; those sacrifices never took away a single sin. Instead, He covered or swept their sins under the rug, as it were, holding them until Christ's blood provided the true atonement and they were forgiven.
Les explains that the Old Testament Day of Atonement was not the appropriate word, because even when the high priest did everything exactly right and offered the blood of the sacrifice on the Holy of Holies and on the mercy seat, it never took away a single sin. It was simply a stopgap waiting for the coming of Christ. The word atonement was a misnomer; it should have had to do with covering, or as Les often says, a sweeping under the rug. That is actually what God was doing with the sins of the Old Testament believer. He swept them under the rug until the true atonement was finalized when the blood of Christ was shed. Then all that was under the rug was atoned for, taken away, and they were forgiven.