Well, that’s partially the point. Bedouin had begun filtering into Syria long before Islam, transforming marginal farmland into transhumance pasturage for herd animals. As they continued to migrate into the region some began settling in towns and became sedentarized. However many continued to live on the fringes of urban settlements, where they often functioned as late-model foederati of sorts, being provided money by the state to function as a protective militia. As early as the third century Fergus Millar in The Roman Near East, 31 B.C. - 337 A.D. ( 1993, Presidents and Fellows of Harvard College ) notes a Roman citizen of ‘Septima Kanotha’ ( a little north of Bostra on the road to Damascus ) self-identifying as an ‘Arab’ in his epitaph. Not so surprising as the province he lived in was Arabia Petraea ;).
Now as it happens the area had undergone some Hellenization early on after its incorporation and said Arab cited above may or may not have spoken Arabic or a Nabataean proto-Arabic. But to quite Albert Hourani’s A History of the Arab Peoples ( 1991, Warner Books ):
The power and influence of the empires touched parts of the Arabian peninsula, and for many centuries Arab pastoral nomads from the north and centre of the peninsula had been moving into the countryside of the area now often called the Fertile Crescent: the interior of Syria, the land lying west of the Euphrates in lower Iraq, and the region between the Euphrates and Tigris in upper Iraq ( the Jazira ) were largely Arab in population.
The coastal and northern Syrian population would have been predominantly Aramaic and Greek speakers, but the southern and eastern fringes of the region were already Arab and largely Christian ( with connections snaking south into central Arabia, where there were Christian and Jewish converts ). While the pre-Islamic Arabian peninsula was largely pagan it was hardly exclusively so. Even in northern Syria Bedouin encampments could be found on the edges of towns, where they functioned as irregular defense against wilder Bedouin. In the 6th century sedentary Arabs in southern Palestine were also hired to guard against Bedouin raiding.
So, nope - some Arabs preceded Islam into parts of Syria, including the Palestine provinces.
ETA: By the way I am not trying to equate modern Palestinians with Roman-era Arabs. The actual truth of the matter is far more complex - the Palestinians of today would be descendants from a whole mix of people, some of whom may not have entered the region until much later. Such it is with many modern populations. I’m just saying that Arabic-speakers did precede Islam into the region.