@fresco,
The Aramaeans were a people speaking a Semitic language who first appear in the historical record more than 3000 years ago. Their descendants are known as Syriacs and we would place Aram, their homeland, in central Syria.
After having gone to war several times with the Hebrews (accounts are confused, but it appears there is some basis for the Biblical accounts of Solomon and King David), they became confessional Jews, which may at first simply have been expedient. The Aramaeans became the most common traders in the middle east and beyond. Aramaic was the
lingua france of the middle east for centuries, both before and after the Greco-Macedonian conquest. The Hellenistic culture may have made Koine Greek the language of the elites and of official documents, but Aramaic continued to be the language with which people from different places and cultures communicated.
They also spread confessional Judaism throughout the middle east, and beyond, into central Asia and as far east as China. When Marco Polo talks about there being Jews in this or that region on his travels, he wasn't blowing smoke. Judaism was the dominant "non-pagan" religious practice of the Arabian peninsula in the seventh century, and had been so firmly ensconced there, and was so widely practiced that Christianity failed to displace it as it did in so many other places.
If Mohammed was not a pagan, about the only reasonable option would have been that he was a confessional Jew.