First of all, Peter died well before the end of the first century. THREE sucessors of his ALSO also died before that centuury ended, so what’s your point?
That STILL would have been “shortly after” Jesus’ earthly life.
Apostolic succession is a man-made plan. They were all convinced that the end was very near so why appoint successors?
Matthew 24:34 I tell you the truth, this generation will certainly not pass away until all
these things have happened.
Matthew 16:28 I tell you the truth, some who are standing here will not taste death before they see the Son of Man coming in his kingdom."
1 John 2:18 Dear children, this is the last hour; and as you have heard that the antichrist is coming, even now many antichrists have come. This is how we know it is the last hour.
1 Peter 4:7 The end of all things is near. Therefore be clear minded and self-controlled so that you can pray.
James 5:8 You too, be patient and stand firm, because the Lord’s coming is near.
1 Thessalonians 4:15 For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord, will not precede those who have fallen asleep. 16 For the Lord Himself will descend from heaven with a shout, with the voice of the archangel and with the trumpet of God, and the dead in Christ will rise first. 17 Then we who are alive and remain will be caught up together with them in the clouds to meet the Lord in the air, and so we shall always be with the Lord. 18 Therefore comfort one another with these words.
1 Corinthians 15:51 Behold, I tell you a mystery; we will not all sleep, but we will all be changed, 52 in a moment, in the twinkling of an eye, at the last trumpet; for the trumpet will sound, and the dead will be raised imperishable, and we will be changed.