But is the Bible the sole or original source? I ask that because the olive branch was apparently also a peace symbol within the separate tradition of classical Greek mythology.

Carl Jung and his followers have noted that mankind shares common symbols (see Jung's book, Man and His Symbols). After taking a course in children's literature some years ago, I realized that fairy tales tell essentially the same stories, despite their having been told in parts of the world with no contact with one another. We have a common human experience. So, now that I've laid bare my limited knowledge, would somebody pass me a fig leaf?