Catholics please explain your Pope?

How is that 440 years after Christ you christen the first pope and then use others in history to complete the succession to Peter? Catholics have a problem here, and can not explain this. 440 years, and then all of a sudden a pope? If your claims of Peter as the first pope were true, then wouldn't of he made a clear succession doctrine of this effect? Not some council who decided to do this 440 years later, which is man-made doctrine by the way, not God driven. Show a specific Bible verse which is God's word by the way even though most Catholics dismiss the Bible to legitimize their false doctrine.