How do we know that Christ's death was a substitution for our sins?

The concept of substitutionary atonement is crucial to understanding Christ’s crucifixion. He bore the penalty for sin that was due to humanity, fulfilling the requirements of divine justice. Colossians 2:14 highlights that He canceled the record of debt that stood against us by nailing it to the cross. Furthermore, 1 Peter 3:18 teaches that Christ suffered for sins, the just for the unjust, to bring us to God. This substitution is vividly illustrated in the account of Barabbas, where the guilty was set free while the innocent Christ took his place. This underscores the core belief in sovereign grace taught in Reformed theology, which asserts that Jesus' death was specifically for His elect.