What was the way of salvation for those living in the times of the Old Testament?

TL;DR:

The Old Testament way of salvation was the same as the New Testament way—faith in God's power to save and His willingness to provide that salvation.

The way of salvation in the Old Testament was faith—trusting in God's power to save and His promise to provide that salvation. Old Testament believers, like Abraham, were counted righteous because they trusted in God's promise of a coming Redeemer, even before Jesus’s arrival (Genesis 15:6; Habakkuk 2:4). Animal sacrifices were commanded as a temporary covering for sin, pointing forward to Jesus’s ultimate sacrifice, but they did not by themselves save (Leviticus 4:27–31; Isaiah 53:5–6; Hebrews 10:10–14). The New Testament reveals that salvation has always been by grace through faith in Jesus Christ, the fulfillment of the Old Testament promises (Romans 4:3; Ephesians 2:8–9). Today, we continue to be called to trust in God’s faithful redemption, knowing He is the same Savior throughout all time.

from the old testament

Faith in God's promises, such as the coming Redeemer (Genesis 3:15; Isaiah 9:6), was the means by which the righteous were counted as righteous, even before the Messiah’s arrival (Habakkuk 2:4).
The Israelites were commanded in the Law to perform animal sacrifices as an atonement for sins (Leviticus 4:27–31; Leviticus 16:34; Numbers 15:25). These sacrifices did not save them; rather, they revealed the people’s sin and their need to be made right with God. However, these sacrifices were not sufficient to totally or eternally deal with the problem of sin. The sacrificial system as a temporary covering for sin revealed one’s faith in God.
People were called to trust in God’s covenant, obey His commands, and rely on the sacrificial system to atone for their sins (Genesis 15:6; Leviticus 17:11; Psalm 32:1–2).
The sacrifices, especially the offering of animals, symbolized the cost of sin and pointed forward to the ultimate sacrifice of the Messiah (Isaiah 53:5–6; see Hebrews 10:1–4).
The Old Testament believers did not see Christ, but they trusted that God would provide whatever they needed—including salvation. They understood that animal sacrifice was only a symbol of God's willingness to forgive and atone for those who recognized their sin and need to be redeemed (Psalm 78:35; Isaiah 41:14). God has always borne the name Redeemer; He has always been a Savior. He is always Himself.
Ultimately, the Old Testament points forward to salvation through God’s grace, fulfilled in Jesus Christ (Jeremiah 31:31–34; Psalm 130:3–4).

from the new testament

For mankind, there has always been only one way of salvation: Jesus Christ, "for there is no other name under heaven given among men by which we must be saved" (Acts 4:12; Psalm 118:22).
The Bible tells us, "Abraham believed God, and it was counted to him as righteousness" (Romans 4:3). Abraham lived long before the time of Christ, but he also lived long before the Mosaic Law was put in place.
The sacrifices of the Old Testament foreshadow, or look forward to, what Christ would do on the cross. Christ's sacrifice was the reality while the animal sacrifices were just a shadow of that reality. This is explained beautifully in the book of Hebrews, which says, "And by that will we have been sanctified through the offering of the body of Jesus Christ once for all. And every priest stands daily at his service, offering repeatedly the same sacrifices, which can never take away sins. But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, waiting from that time until his enemies should be made a footstool for his feet. For by a single offering he has perfected for all time those who are being sanctified" (Hebrews 10:10–14).
Abraham was saved by faith in this process, just as those under the Law were saved, and just as we who are now under grace are saved. The next chapter of Hebrews, chapter 11, enumerates the many people throughout the Bible who were saved by faith in God's work.
The Old Testament way of salvation was the same as the New Testament way—faith in God's power to save and His willingness to provide that salvation (Romans 1:16; 1 John 4:14).

implications for today

Throughout history, salvation has always been by faith—trusting in who God is and what He promises. In the Old Testament, people like Abraham were counted righteous because they believed God's promise of a coming Savior even though they didn’t see Him yet (Genesis 15:6; Habakkuk 2:4). The animal sacrifices were not the solution but symbols pointing to Jesus’s ultimate sacrifice on the cross (Isaiah 53:5–6; Hebrews 10:10–14). Like those early believers, we, too, are saved by placing our faith in God’s power and His grace, not by our own efforts (Romans 4:3; Ephesians 2:8–9). We, like those living in the times of the Old Testament, are called to trust in God, confident that He is the same faithful Redeemer who fulfills His promises through Jesus Christ.

understand

Salvation in the Old Testament was by faith—trusting in God's power to save and His promise of a coming Redeemer.
Animal sacrifices in the Law were symbolic coverings for sin that pointed forward to Jesus’s ultimate sacrifice but did not themselves provide eternal salvation.
The New Testament confirms that salvation has always been by grace through faith in Jesus Christ, fulfilling Old Testament promises and offering the only true means of redemption.

reflect

How does knowing that salvation has always been by faith, even before Christ’s coming, affect the way you trust God today?
How do you see the Old Testament sacrifices pointing to Jesus’s sacrifice, and how does that deepen your understanding of grace?
How do you respond when you remember that God has been faithful to His promises throughout all of history, including the times before Jesus?

engage

How might understanding the Old Testament way of salvation by faith change how we explain the gospel to those unfamiliar with the Bible?
How do the Old Testament sacrifices enrich our appreciation for Christ’s ultimate sacrifice on the cross?
How does recognizing the continuity of God’s plan for salvation from the Old Testament to the New Testament influence the way we live out our faith today?