Did killing Jesus stop God's program?
No. The crucifixion did not stop God's program, because God raised Jesus from the dead. He is still alive, and Peter made this known. Even though the nation demanded it and caused Rome to carry it out, Israel was called to repent of rejecting their Messiah, proving repentance with baptism.
Les explains that Peter was still addressing only the nation of Israel on the same covenant ground as before the crucifixion. Peter charged the nation with having killed their Messiah, though they did not do it with their own hands—they demanded it and caused Rome to carry it out. But killing Him did not stop God's program, since God raised Him from the dead and He is still alive. Peter therefore called Israel to repent of rejecting their Messiah, and to prove that repentance with baptism. Les also notes that Peter says nothing here about a Gentile.
Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.