What explanations are there for God's lack of culpability for the sin that was a part of the plan of salvation?

Acts 2:22-24 NET says: > 22 “Men of Israel, listen to these words: Jesus the Nazarene, a man > clearly attested to you by God with powerful deeds, wonders, and > miraculous signs that God performed among you through him, just as you > yourselves know— 23 this man, who was handed over by the predetermined > plan and foreknowledge of God, you executed by nailing him to a cross > at the hands of Gentiles. 24 But God raised him up, having released > him from the pains of death because it was not possible for him to be > held in its power. 1 Peter 1:18-20 NET says > 18 You know that from your empty way of life inherited from your > ancestors you were ransomed—not by perishable things like silver or > gold, 19 but by precious blood like that of an unblemished and > spotless lamb, namely Christ. 20 He was foreknown before the > foundation of the world but was manifested in these last times for > your sake. 21 Through him you now trust in God, who raised him from > the dead and gave him glory, so that your faith and hope are in God. These passages and others clearly indicate that salvation through the crucifixion, death, and resurrection of Jesus was the plan from the beginning. I'm concerned specifically with the plan of salvation since it is defined explicitly as a detailed plan from the beginning. That means that the sin of those involved in enabling the crucifixion was a part of the plan from the beginning: Judas's betrayal, the condemnation by the Jewish elite, etc. Succinctly, this means that, from the beginning, sin was a part of the plan to save us from sin. What explanations are there for this that address the logical conclusion that God is the author of the sins included as part of his plan for salvation, via the crucifixion of Christ, from the beginning?