How do we know that Christ's death was a substitution for His people?

Christ's death is the cornerstone of Christian faith, as exemplified by His role as our substitute. The Apostle Peter writes that Christ suffered for sins, the just for the unjust, to bring us to God (1 Peter 3:18). This demonstrates that Christ endured the wrath and judgment we earned due to our sins, similar to how the Ark bore the judgment of the flood without harm to those inside. By bearing the penalty for our sins, Christ fulfills God’s justice, allowing believers to be declared righteous before Him, as Paul asserts in 2 Corinthians 5:21.