I've came up with another strategy which gave me even better results. It probably does require a decent starting location though. The key is going for the classical golden age with strong faith output (I even got a religion). Egypt is literally build for early monumentality because they can generate the faith with desert folklore (desert bias) and the sphinx. Settlers, builders and traders are also cheaper to purchase with gold which is obviously amazing for commercial hub spam and Egypt's bonuses!!
Starting location (Settler on plains hill and two 2/2 tiles in 1st ring, pretty good!), save file is attached:
With Monumentality, the 3rd settler only costs 390 gold instead of 440, I bought the 4th one for 205 faith! This way you have 4 cities relatively early but only have to produce 1 of them. The timing works best on Deity because the classical era starts earlier. On lower levels, it's easier to reach the golden age though.
My religion (I got the 2nd to last prophet on turn 54):
Screenshot turn 100 with 9 cities, a religion (no 2nd prohept yet) and 200 gold per turn (including 90 gpt from a peace deal) and rising (2 unfinished markets and harbor)! :
How did I get the +24 era score for the classical golden age?:
1. Destroy two barb camps: +6
2. Make contact with three civs: +3
3. Four goodie guts: +4
4. Holy site with +5 adjacency: +3
5. Sphinx: +4
6. Settle on a desert tile: +1
7. Build campus with +3 adjacency: +3
If you need more points, you can also:
1. Build a Mayannu: +4
2. Find a city state first and send Amani: +2
Build Order:
Capital: Scout Scout Slinger Settler, Builder, Holy Site, Shrine, Prayer project
2nd city: Rushbuy Monument, Builder -> Holy Site -> Shrine -> Slinger -> chop Campus (use Magnus and overflow if you want to get the best results)
After that: Military with Agoge, rushbuy trader and send it to the scientific CS preferably for the +2 science per turn.
Double Scout for getting early era score, Slinger (or Warrior) for clearing barb camps,
2 monuments are necessary for getting Amani/Magnus in time for either Mayannu/district chopping or CS era score.
Tech Order: Astrology (can abort if you don't find a natural wonder in time but don't wait too long) -> Mining -> Wheel (for Mayannus) -> Writing -> Currency (unless you really need Animal Husbandry/Irrigation/Archery)
Civic Order: Foreign Trade (switch to Craftsmanship if you don't find a 2nd continent) -> Craftsmanship -> Early Empire -> Mysticism if you need that envoy/Amani to get more era score
Next steps: Pick Monumentality golden age, rushbuy 3rd settler, faithbuy 4th settler, found the religion, build Commercial Hubs, build Mayannus with Agoge and use the overflow to chop markets with Magnus, either spam more Mayannus and attack your neighbour or expand with settlers and faith-/rushbuy builders/traders whenever possible. In my game I went for a hybrid. I used 3 Mayannus and took 2 cities from Korea and made a good peace deal. Meanwhile I built one settler in each of the 4 cities (with the +50% settler card).
After that try to get the medieval golden age (science from commercial hubs) by using Amani, settle one city on the coast for the +2 era score from a galley, found and expand the religion etc.
Ideally all your trade routes should go to a scientific CS or a civ like Korea to counter the lack of early campuses.
Religion:
1. With choral music and two early shrines, you get +4 culture. Pretty good. Culture progression doesn't slow down.
2. Defender of the faith: This is debatable of course but it's a very nice passive bonus, even for conquering. Mayannus are already strong but with +10 combat strength, you are 100% save from any possible AI attack.
Government: As government I chose Autocracy (nice early boost and you can switch to classical republic a little later) and Audience Chamber (I needed the housing to grow my core cities and Egypt can rushbuy builders anyway).
Governors: For chaining two early golden ages, I think Amani is more useful than lvl 2 Magnus. On this map I didn't really care about losing population because housing was an issue. So the order was Magnus -> Amani -> Liang
I also attached the save file if anyone wants to try the buildorder on this map. Standard speed, standard map size, continents, Deity.