I can't say that there were no domestic pigs in Arabia before Islam, but, for instance in Robert Hoyland's Arabia and the Arabs: From the Bronze Age to the Coming of Islam the words "pig" "pork" and "boar" are not mentioned.

Even if there hypothetically were pigs in Arabia there are only a limited number of locations where they could plausibly have been raised, such as in Yemen or the southern Levant. The raising of pigs, as I understand it, is a sedentary form of pastoralism. This would have been less common in Arabia than transhumance (i.e. seasonal migrations) or nomadic pastoralism. These latter forms focused on the raising of goats, sheep, and, most famously, camels.

Nor am I familiar with any reports of food shortages associated with Islamic strictures on food consumption.

Domestic pigs can be found in Ancient Egypt dating back to the 5th millennium BCE, and were extremely common throughout North Africa until Islam became dominant, and was still common amongst some of the Berbers until relatively recently.

One of the primary purposes of pigs is garbage collection, as such while owning Pigs may have been outlawed for the Muslim population, there is still a need for them and some level of tolerance of letting marginalized groups have them. To this day, the Egyptian underclass of informal garbage collectors, the Zabbaleen, still use and grow pigs. They are also over 90% Coptic Christian. In times of religious fervor and hysteria over disease outbreak it has not been uncommon for the government to do cullings, including as recently as a few years ago.

As for the food issue, just like today, people thousands of years ago preferred beef to pork. People, especially the poorer, ate more pork when beef was less available. McDonald's does this as well, when beef futures are expensive they bring back the McRib.

The problem of pigs is not that they're dirty or carry disease, that's 'mostly' a problem of modern farming. It's that they're bad nomadic pastoral animals, and bad at herding across deserts (though they travel by boat fine). Pigs are actually pretty smart and if given enough space will avoid sleeping in their own filth.