And eventually the church saw the importance of commemorating it. In choosing a date, obvious recognition was given to the pagan celebration Saturnalia. I'm not sure a cynical interpreation of this act is warranted. We don't know precisely when. The4se are hotly debated questions even today.
Major religions predict the arrival on the scene of a new world teacher soon.
That's an interesting question, and I suppose it is a possibility. I haven't heard of it, though. A martyr, never left writings, had followers, etc. It's safe to say that without the martyrdom of Jesus, Christianity would not have gone anywhere. Jesus's teachings did not become Christianity until after his death Resurrection.