It is true that Old Testament believers lived before Jesus' actual historical sacrifice, yet the Bible suggests that they experienced acceptance and fellowship with God on the basis of their faith in what God had revealed of Himself and His ways. Genesis 15:6 says concerning Abraham: "Abram believed the Lord, and he credited it to him as righteousness."
The Old Testament makes clear that God taught the people to approach Him by way of animal sacrifices. The Mosaic Law required that animals be offered as sacrifices and that the priests sprinkle the blood upon the designated altar. Those sacrifices foreshadowed and symbolized the anticipated shedding of blood and sacrificial death of Jesus, the Messiah.
Christ's eventual sacrifice of His own life as the "lamb without blemish" was the fulfillment of the sacrificial offerings to atone for sin. The Old Testament book of Leviticus and the New Testament book of Hebrews provide an excellent harmony of truth on this subject.
Both Old Testament believers and New Testament believers were saved by grace through faith on the basis of the shed blood of Jesus Christ. The Old Testament looked forward to the sacrifice of Christ, while the New Testament looks back on that same sacrifice.
Throughout the history of this world, countless people have discovered that God alone, through Jesus Christ, can meet the deepest longings and needs of the human heart. This is possible because Jesus was fully God and fully man. He died to pay the death penalty for our sin, and He was raised from the dead by the power of God. He is alive today, and He wants to be in your life right now. We encourage you to commit your life to Christ. It is the most important step you will ever take.