"Salvation comes through Jesus alone."
"How were people saved in the Old Testament before Jesus paid for our sins on the cross?"
When we get to heaven, we will find that every believer has been saved through faith in the shed blood of Jesus Christ—whether they lived during the Old Testament period or the New. Old Testament saints, who lived thousands of years before Jesus' crucifixion and resurrection, such as Moses and David, looked forward by faith to the promised Savior who would wash away sins. Even Abraham saw the promise of Christ from afar and lived by faith in this promise until his death (see Hebrews 11:8-16). And when his descendants, the Israelites, saw a lamb slaughtered, they too had faith that God would provide the sacrificial lamb to atone for their sins. Indeed, the sacrificial system God gave the people constantly foreshadowed the promised suffering Messiah, the Lamb of God.
For us living in the New Testament, we are saved by that same faith as we look backward to the apex of history—the sacrificial death of Jesus Christ. So whether in the Old or New Testament time, it has always been one faith, one God—salvation comes through Jesus alone.