May I suggest adding “time-lime” to this story?
Without dates it is not a ‘history’ but a ‘legend’ and there is evidence of (organic matters/fossils) to support the theory that ‘the [desert] area’ was once a fertile land. See
Earth - Arabia was once a lush paradise of grass and … - BBChttp://www.bbc.com/earth/story/20150223-arabia-was-once-a-lush-paradise
…“We have evidence that humans managed to expand out of Africa and into the Middle East between 130,000 and 90,000 years ago,”