The last I looked, studies of (surviving) hunter-gatherer cultures and remains indicate that they were both better nourished and had more free time than farmers. The real difference is the population density supported. It wasn’t the handful of roaming hunter-gatherers per 100 square miles who were at the mercy of the weather; it was the farmer, tied in place by his farm and storage structures (try transporting a years worth of food, planting seed, tools, etc. per worker), dependent on the success of every single growing season to feed 100x as many people on the same land. Even today, it is the farmer who rises to the weather report and sleeps planning for next week’s weather. So long as plants/animals could still inhabit a region, a H-G had a reasonable chance, at a suitably low density.
And the leisure time of a H-G society leads to art (e.g. the highly decorated and finished batons of nomadic Neanderthals) but not of the large scale installation/construction types (murals, frescos, elaborate weavings vs hand knotting) that suits farmer thinking. Of course, it can happen, if a suitable place presents itself: IIRC, cave paintings at Lascaux, etc. don’t celebrate the gods of agriculture, such as wind or weather.
Neanderthals were far more sophisticated than most people give them credit for. They apeear to not only have culture, as we know it, but successive waves of cuture sweeping across continents. Following the links on Wikipedia gives a fair overview, though the last time I checked tehre wasn’t a good single overview.
So, to me, the question is specialization. The best flint-knapper in the tribe probably spent time in the haunting parties like everyone else, as long as he was able, and taught the others how to knap better as well – but they probably didn’t have the modern notion of “quality”: a tool that was better was likely to be attributed with superior mana, not superior workmanship (so the rate of improvement and spread of improvements was slow, we’ve found pockets of distinctly better tools, that took thousands of years to catch on and spread). A craftsman who stood head and shoulders above the others might be considered more like a shaman than a toolmaker.
So when we say “first profession”, I think we mean someone who earns all or most of his/her living through a single set of skills. A hunter who wouldn’t spot and gather berrries would likely be a poor hunter. Society makes “prostitutes” by limiting the availability of mates; it’s not as viable a long term lifestyle, because it relies onthere being a surplus of food and good. In hard times, or old age, the mates are more likely to eat.
A farmer is also a toolmaker, builder, etc., even today to some degree: Farmers can’t afford to hire contractors to put up fenses, fix the barn and keep the tractor going. t’s just not cost effective when things aren’t going well. A farmer is more likely to know their way around an arc-welder, a post hole digger, a hammer or a wrench than a hunter – or have a friend who will help them: farmers, being tied in one place in communities, rely as much on shared skills and social bonds as commerce.
So, though I didn’t think so at first, after some thought I think that the oldest profession may indeed have been shaman, because a person who had “a special relationship” with the unknown forces of the universe, and specialized in only one activity might well have been seen in a lght akin to the modern image of wizard/shaman than the modern craftsman. Most mythologies have craftsmen/wizard gods/demigods (often crippled and therefore unable to perform the normal activities of the other gods, which might be how they became so specialized) alongside the rest of the pantheon.
We think in terms of specialized jobs/careers. I think that colors our guesses. A hunter gather was much more a generalist, and any person who supported themselves primarily through a specialized skill rather than the “normal activites of daily living” (hunting and gathering being a normal task for even children in that lifestyle) would need a certain reputation to gain a clientele, especially in low population densities. One might well walk miles (walking being a normal HG activity, an ot a chore) and bring food to the flint-knapping wizard, when the hunt was going badly or a “magic” or “lucky” spear broke.
I’d make a distinction between roaming HGs (roaming widely as individuals, and moving as family-sized units when conditions required) and the intrinsically nomadic tribes (e.g. nomadic herdsmen constantly moving their heards to greener pastures).
Trade, likewise could have been specialized. There would have been incidental “contact trade” of course, but this requires either nomadic groups (supporting themselves as HGs or herdsman) or two adjacent communities with reliable suplies of distinctly differnt goods to trade. Few mineral deposits would have qualified, I doubt crops would have differed much either. I think that trade could not be viable as a profession except over larger distances until craftsmen were common. While salt and flint were among the first valuable trade goods, it is not clear that a population would mine (or produce, in the case of sea salt) or produce such materials on a large excess scale until there were ample supplies of goods they greatly desired, and sufficient local food supply to assure their survival year to year. Professional itinerant traders could have filled this niche – but I think the "home grown shaman/craftsman/wizard would have predated the professional trader