Romans 3:25 essentially point blank answers this question:
Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God.Before Christ those who trusted in the coming Messiah were saved by His grace. They believed God's Word regarding salvation, which is the everlasting Gospel (Rev. 14:6). Those who believed in the Messiah, according to the revelation God gave them, put faith in the blood of the Lord Jesus Christ and their sins were remitted, that is, disregarded until they were declared righteous upon Christ's death. The Lord's death and shed blood propitiated (satisfied) the righteous justice of God. God remitted or passed over the sins of Old Testament saints based upon His forbearance.
Let's say that I owed a huge debt to someone whom I could not repay. However, I knew someone who I was 100% sure would pay my debt at some point in the future, so I came to the one to whom I owed my debt and asked for mercy based upon the reputation of the one who could and would pay my debt. Old Testament saints owed a debt. Jesus could and would pay the debt. The Father would remit their sins through their faith in the future Messiah, His Son. He would forbear, holding back His righteous judgment, until the day that His justice was satisfied by Christ's debt payment on the cross.