I disagree. I think it was Arabia Felix during the Climatic Optimum, 4500 years ago. Rainfall was abundant, and both Arabia and Libya were grasslands with flowing water. Then the atmosphere began to cool a few degrees, and desertification set in as the southerly monsoons died out and the trade winds became established in the tropics.
The resultant desertification of Arabia sent successive waves of Semitic husbandmen both north and south in search of adequate pasturage: across the Red Sea in one direction, and into the Fertile Crescent in the other. Which is why Abraham was born in Ur of the Chaldees. He was an Amorite, of the band called Habiru, or "Hebrews" to us.