How do we know that Christ was made a curse for us?

In Galatians 3:13, it's explicitly stated that 'Christ hath redeemed us from the curse of the law, being made a curse for us.' This is grounded in Old Testament Scripture, such as Deuteronomy 21:22-23, which explains that anyone who is hanged on a tree is cursed by God. This demonstrates that Jesus, who was sinless, took on the sins of His people, thus absorbing the curse meant for them. By doing so, He not only fulfilled the law but also provided a means for salvation, thereby transforming the curse into a blessing for those who believe in Him, aligning with the broader narrative of Scripture.