The dying of Jesus on the cross, is the basis upon which we are redeemed from suffering the penalty for our sins. Jesus' sacrifice is the basis upon which God can save us. God's holiness demands that the penalty for sin, all sin, be paid. God's grace has provided the perfect sacrifice to cover our penalty.
Believing is a condition whereby God can count Jesus' sacrifice sufficient to cover our penalty for sin. Believing, faith, was counted to Abraham as righteousness.... the promise to Abraham and his offspring that he would be heir of the world did not come through the law but through the righteousness of faith (Rom 4:3,13)
The dying didn't save us. If that were the case, then all would be saved. We are saved through faith. We are saved, not by believing, but through believing.