No, you don't need agreement for any of this to happen. In fact quite the opposite, we know today that original christians (at the time of Paul) were at odds in practically anything, including the idea that Jesus came in flesh (you will find this being condemned in the new testament itself).
However, from several branches of this fringe cult one won out over time, the one started by Paul (who never knew a real Jesus, as he confess by the way). This one branch created a single story (the Gospel of Mark) that was copied and embellished by several others. This is the one version of Christianity that became famous and powerful.
So we don't have them all agreeing on the basic facts, as you mention. We have a story that was created and embellished, and them every other dissenting voice was suppressed.