How do you show a Protestant that apostolic authority really was passed on to the Church?

Naturally, if you are a Protestant without apostolic succession, you will try to twist the evidence to show there is none. But look at the Old Testament: the kings followed one another, and you see no explicit command of succession, because it was simply the natural thing to do; obviously if a king dies you replace him. They even had the 'master of the palace,' a figure like a chief of staff who served under the king, kept the king's house, and was replaced by a new one when he died, sometimes outlasting the king himself. Eliakim was such a master of the palace, and that role is basically the same as St. Peter's: Peter is the master of the palace for Jesus Christ, the head of the Church. And it was established from the start: Acts 1:20 has Peter replacing Judas by quoting the Old Testament, Psalm 109, which says 'his office let another take,' so they restored the number to twelve, the apostolic number Jesus established. How did Peter know to go to that Psalm? Someone was guiding him; during the forty days after the Resurrection, Jesus was alone with Peter teaching him how to run the Church, including that Judas had to be replaced. Then Paul tells Timothy he received his office by the laying on of hands. So succession was there from the Old Testament and was only enhanced in the New; a Protestant has to deny it, because if he does not, his whole religion falls apart.