I wrote a very long and detailed answer on this from a Roman perspective here. It is also worth emphasising that the Arabs were not just desert nomads, as some Arabs on the frontiers had also played a key role in the armies of Rome and Persia in late antiquity - these Arab auxiliaries' primary job was to defend imperial territories from Arab raiders and they had continued to serve their respective empires during the conquests too, so I don't think either empires were too surprised to be attacked by nomads. There were also Arabs deeper into Arabia who lived in urban settlements, take for example Muhammad and the towns of Mecca and Medina. Even people who didn't live in these settlements would have been aware of the wider world, since everything was interconnected. There was for instance a series of conflicts in the sixth century that saw Rome, Persia and Ethiopia repeatedly intervene in the politics of south Yemen. These external powers also played off various Arabs groups against each other, so we shouldn't see the rise of Islam as the rise of an 'Other', but a movement/polity that was very much in tune with its late antique intellectual and political milieu. Many Arabs were indeed nomads, but Arabian society as a whole was a great deal more complicated than that and their success was I think due to a combination of factors, with the lifestyle of some tribesmen being only one cause out of many for their extraordinary triumph over the two superpowers in the region (I've written a post on this as well, I think it could do with an update when I have some more time though...). Let me know if you any more questions!