It may have been said before but this time I'd like to present something probative (as they say on CSI) along with it.
Archeology. In the "Fertile Crescent" of the Levant, several sites have been excavated showing the development of the first agrarian culture.
At one of the oldest, Ain Ghazal, there is evidence of ancestor worship. Grandad is buried beneath the hearth to keep him warm, or skulls are lined up on a shelf to remind people where and who they come from.
Slightly newer is Djouf el Ahmar, the earliest know public building cum temple, which probably had some kind of full-time staff. Separate from the surrounding villages, it may well have been intended as a focal or unifying point. It was also destroyed in a violent attack. Revolution or religious war, we may never know.
At Talayat Ghassul the process is clearly complete. There is a mural preserved showing a religious procession with the local aristocrats and priests in funny masks leading the way.
Society had at this point come as far as producing a surplus which a minority was determined to get its grubby hands on and keep. The most effective way was, of course, a paid class of propagandists. For a tenth of the profits you buy a prophet and the unruly rabble are kept in their place.
Of course, as time went by the God Squad got above themselves and became king-makers and breakers but that's what makes up a lot of the Old Testament.
This, I do contend, tends toward proving my point. The priesthood is the oldest known profession, although they don't brag about it much.
As for the traditional job: the first prostitute named in world literature is Shamhat in the Gilgamesh epic, who was a [i]temple[i] pro. So which came first there?
The archeology is something I've taken from that excellent Aussie/Welsh TV documentary series "Stories from the Stone Age". Well worth watching more than once.