I don't think it is independent discovery, because Christianity was born at a time when Greek ideas were widespread (Palestine having been a Greek-dominated area for centuries before the arrival of Romans). I believe there was an amalgamation of elements from ancient Hebrew religion with other pagan myths mainly from Greece.

"Independent" may have been overstating it, I just think something is being lost when we frame one religion (or even a subset of its concepts) as being purely derivative of another. Just because ideas are similar doesn't necessarily mean they have the exact same origin, and in fact I think it's much more interesting to look at the cases where they didn't have the same origin, because it tells us something about ourselves as human beings.