I doubt, however, that anyone out in rural Palestine of 0 BC was speaking Greek so the origins should be somewhat more obscure.
The root was likely borrowed from Aramaic or Hebrew. However the origin of the genitive itself is Greek - unlike Latin, Greek typically didn’t borrow full declension tables, it borrowed the root and plopped a native Greek declension. And that’s clearly the case here, none of the Semitic languages use an -s for the base form, so Greek changed even the nominative:
The root was likely borrowed from Aramaic or Hebrew. However the origin of the genitive itself is Greek - unlike Latin, Greek typically didn’t borrow full declension tables, it borrowed the root and plopped a native Greek declension. And that’s clearly the case here, none of the Semitic languages use an -s for the base form, so Greek changed even the nominative: