How do we know Christ's death is a substitutionary sacrifice?

The nature of Christ's death is crucial to understanding the gospel. The Apostle Paul emphasizes that Christ died in the stead of all whom the Father elected, as mentioned in 1 Peter 2:24, which states, 'who his own self bare our sins in his own body on the tree.' This highlights the doctrine of substitutionary atonement, where Christ took upon Himself the punishment due to His people for their sins, satisfying God's justice. Thus, His death not only represents a historical moment but the very means by which believers are justified, as illustrated in Romans 5:8’s assertion that 'God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.'