At what point of the crucifixion did Jesus take on all the sins of the world?
Christ’s physical death on the cross was important, yet it was just one moment in a series of events that collectively were His redemptive work.
First, Christ was publicly displayed by the Father as our substitute, our “scapegoat,” bearing our guilt during His cruxifixction experience:
Christ’s tortuous death experience was collectively an exercise in bearing our punishment publicly, as Paul says:
Christ's public humiliation was made necessary for our sake, Paul says, so that we (i.e., the public) might recognize the Lord at work exacting a price for the sins He previously passed over. But Christ’s painful humiliation was only the beginning of His redemptive work. His cruel torture was not a sufficient payment for sin by itself.
So Christ also had to die spiritually to take the curse that God pronounced on sin in the Garden. God told man that a “death” (i.e., spiritual separation from God) would be the penalty for disobedience to God’s word:
The word “die” in that context doesn’t refer to physical death but rather spiritual death. So Christ had to take our place in spiritual death in order to be our propitiation. The moment of His spiritual death occurred prior to Christ’s physical death on the cross, when the Father turned His face from Jesus:
For three hours Jesus was separated from the Father’s love, which must have felt like an eternity to the sinless Son of God. Near the end of that three-hour period, the Son cried out asking why the Father had forsaken Him? Jesus’ question was not a reference to His crucifixion in general but specifically to the darkness, to the absence of the Father’s love which manifested as an absence of light.
As the darkness ended, Jesus’ separation from the Father ended too. Jesus was spiritually reunited with the Father and the second part of His atoning work was complete. In fact, consider the following statements Jesus made from the cross after the period of darkness had ended:
The eternal separation from the Father was finished at that point, and who having been reunited with the Father, Jesus could command His Spirit into His Father’s hands. Christ’s spirit separation from the Father was important, but it too wasn’t sufficient to atone for our sins.
At that moment Jesus’ physical body died, the next part of His redemptive work began. Specifically, the death of Jesus' body on the cross accomplished three things.
First, it made possible His resurrection after three days, which fulfilled prophecy and served as a sign to prove His claims of deity:
Secondly, His physical death made possible His spirit’s journey into the depths of Earth to join the captives (i.e., OT Saints) awaiting Him in Sheol so He could set them free:
Finally, it allowed Him to preach against the evil spirits held in torment:
After Jesus’ had fulfilled Scripture by spending three days in the grave, He was resurrected so He could perform the final – and most important – part of His redemptive work. Jesus traveled in bodily form into the Heavenly realm to apply His blood on the mercy seat in the Heavenly tabernacle. This application of His perfect blood was the moment Jesus made atonement for all sin:
Having applied His own blood to the mercy seat in the Heavenly tabernacle, only then was Jesus’ atoning work complete:
So the atoning work of Christ took several steps beginning with His public shaming on the cross, His spiritual separation from the Father, His physical death and resurrection, and His application of blood in the Heavenly tabernacle.