How do we know the concept of substitutionary atonement is true?

Substitutionary atonement is a central theme throughout the Bible, showcasing how Jesus Christ serves as our substitute, taking upon Himself the sins of His people. As illustrated in Exodus 13:13, the firstborn unclean animals needed a lamb for redemption, which foreshadows Christ's ultimate sacrifice. By dying in our place, Christ satisfied the demands of God's justice. The doctrine is affirmed in several NT texts, such as Romans 3:25 and 2 Corinthians 5:21, which articulate the idea that our sins are imputed to Him, and His righteousness is imputed to us, ensuring that believers stand perfect before God.