How do we know that Jesus' sacrifice was for our sins?

The doctrine of substitutionary atonement is rooted deeply in scripture, as seen in Isaiah 53 where it states, 'He was wounded for our transgressions; he was bruised for our iniquities.' This underscores that Jesus took on the punishment due for our sins. Additionally, 2 Corinthians 5:21 tells us that 'He made Him sin for us who knew no sin, that we might be made the righteousness of God in Him.' This solidifies the understanding that Jesus' sacrifice was intentional and for the very purpose of redeeming humanity by taking our place on the cross.