Jesus came to earth with the purpose of dying on the cross of Calvary as the Lamb of God who takes away the sin of the world.1 That Jesus was arrested, and crucified, did not come as a surprise to Him. In fact, He often spoke of this prior to it happening.2
Keep in mind that Satan is the one who enticed Judas Iscariot to betray Christ Jesus, not God.3 Satan was able to do this because of Judas Iscariotís hardened heart. Although God is not the One who enticed Judas Iscariot, God will use the sin in man to bring about His purposes.
Jesus' purpose, at that time, was to die on the cross of Calvary as the sacrificial Lamb of God to atone for the sin of the world when sin was judged. God allowed Judas Iscariot's betrayal to fulfill this purpose.
1 (Hebrews 10:5-10, 9:26-28)
2 (Matthew 16:21)
3 (John 13:2)