How do we know Christ's suffering is a substitute for our sins?

The doctrine of Christ's substitutionary atonement is firmly rooted in Scripture, particularly in Isaiah 53, which describes the Messiah bearing our griefs and sorrows. Verse 5 clearly states, 'He was wounded for our transgressions; he was bruised for our iniquities.' This points to the reality that Jesus was sinless yet took our sin upon Himself, fulfilling the requirements of the law for us. In Romans 5:8, we read that 'God commendeth his love toward us, in that while we were yet sinners, Christ died for us,' reinforcing the notion that His suffering was for our benefit, making Him our substitute.