Was Israel's offer of the king during Jesus' earthly ministry a genuine offer?
Yes. The offer of the King during His earthly ministry was valid: Israel could have received Him as King, and God in His providence would still have accomplished the necessary sacrifice. God's foreknowledge that they would crucify Him did not make the offer insincere or invalid.
Les explains that the offer was genuine because it was like Israel's earlier opportunity to take the Promised Land: God said it was theirs for the taking, a valid offer, yet they rejected it in unbelief. In the same way, the king was a valid offer first in His earthly ministry. Israel could have had the King, and God in His own providence would still have taken care of the sacrifice that had to be accomplished. However, God in His foreknowledge knew they would crucify Him. After the crucifixion, Peter again presented the nation with the King and the kingdom, and again they rejected it in unbelief, objecting that nothing good could come from Nazareth and that a king should not come on a colt of a donkey rather than a prancing white steed. They continued rejecting Him until God raised up the apostle Paul. This fit Israel's Old Testament prospect of being a light to the Gentiles and a nation of priests.