Long-distance trade is evidenced from the late Neolithic and the very first city-like concentrations, so Commerical Districts should be available very early.
No,
markets should be available very early. Commercial Districts can wait until the Renaissance Era.
Several early cities, notably Uruk and Babylon, started as Religious Sites which collected permanent population later, so the Holy Site actually pre-dates cities.
Holy Sites are certainly one of the districts you could justify having very early.
A related concept I actually had was that you could build certain individual buildings on the map, produced by the city but otherwise similar to improvements - the tile could still be worked, it didn't count as urban, etc. One of those buildings would be the Shrine, where later on (after unlocking it), you could place a Holy Site on top of that tile to turn it into a district.
The earliest attempts at Imperial States (Akkad, Assyria, Hittites, New Kingdom Egypt, Qin China) all had some form of standing army, so Encampments of some kind are also a very early potential District.
And Encampments would make sense by the time of the Classical Era, probably. But again, just because the concept exists that does not mean it has to be represented
as a district.
Trade by Sea and exploiting coastal waters for food and resources, building boats that were at least coastal sea-worthy has now been pushed back in places to Pre-Start of Game or early Ancient Era, so ditto for Harbors (earliest found stone jetties, piers and warehouses: 2500 BCE in Egypt, fired brick versions in India 2000 BCE)
Same as with Commercial Hubs. Just because it happened, that doesn't mean you need a district for it. You need a district when something becomes
large-scale.
Going through Civ VI's full list of districts, here's where I'd argue they should be unlocked (with, for the later unlocks, individual buildings associated with that theme not requiring a district):
Holy Site: Ancient.
Campus: Medieval.
Preserve: Atomic.
Harbor/Port: Renaissance.
Encampment: Classical.
Commercial Hub: Renaissance.
Entertainment Complex: Modern.
Theater Square: Classical.
Dam: Modern.
Industrial Zone: Industrial.
Water Park: Modern.
Neighborhood: Industrial.
Aerodome: Atomic.
Spaceport: Information.
Government Plaza: Classical.
Diplomatic Quarter: Renaissance.
Aquaduct and Canal should not be districts in the first place. They are lines, not blobs.
This provides the count:
Ancient: 1
Classical: 3
Medieval: 1
Renaissance: 3
Industrial: 2
Modern: 3
Atomic: 2
Information: 1
Of course, all of this is assuming districts work like they do in Civ VI in the first place. I'd personally prefer they do away with the level of themed-ness that Civ VI had. For example, there is a decent overlap between buildings that provide entertainment and buildings that provide culture. I think districts should have more to do with how things are organized in the real world, and less with the yields available in-game - those yields are just what fits the districts you're building, rather than the guide for what districts you can build.
The sheer in-game utility of having individual buildings visible on the map in a city is just too great.
It's fun, but it is
insanely limiting. It becomes incredibly difficult to add new buildings where they are thematically appropriate (there's no slot for them to go) or to use asymmetrical design (e.g. a district that has
not precisely three buildings in it). This is one of the biggest flaws of Civ VI imo. The need to represent every last building on the map makes the gameplay around buildings far too simplistic and severely lacks in immersion. For all that I prefer Civ VI over Civ IV, Civ IV
absolutely has superior immersion, and it comes primarily from the lack of symmetry in it's design.