Introduction
I tried different approaches to achieve a fast culture victory with Sacred Sites (reformation piety policy) and I managed to get a T170 one, although I think there is much room to improve and I'm sure that better players can get nonsense win dates. No special starting spot and only fast pyramids as a risky component (not necessary but useful, if faiure just build another worker and buy one with the gold but shouldn't happen on emperor though). Oracle is also very useful to get the reformation belief faster, as we start it soon shouldn't be a problem.
I don't think this strategy works on Inmortal/Deity with Byzantium, because:
a) AI culture output is higher and I think it can surpass your tourism output.
b) You can fail to get the 3 follower belifs of faith buildings
c) You can fail to get Sacred sites as reformation belief
Maybe with Maya or Ethiopia that can found/enhance religion faster than Byzantium can do it with 2 buildings follower beliefs at higher difficulties, dunno yet. Even skipping liberty to focus piety and hard build without bonus all your settlers is also an option, but as you want to spam cities I think it wouldn't work.
Of course I didn't invent nothing, this strategy is quite obvious but in case you didn't know how to do it properly here are some tips. it is a really fun way of playing.
I tried a more secure/solid approach, made my cities grow, go up my science, production and gpt to have some army and flexibility in case the AI got mad with my ubber expansion and needed to defend.
If you keep spamming cities and only producing monument shrine temple colosseum/circus ignoring science (you don't need that many techs), production and don't stop spamming cities due to happiness I guess you can get faster results but it is a lot more risky because your science and production will fall and you can go negatives in gpt.
UPDATE:
Egypt stupid approach. No NC, no universities. Spam cities and build Burial Tombs.
Won T152 with 22 cities. Capital with marble but after Pyramids I build no wonders. Engineer points gave me one and I had him sitting there 
Spoiler :
Other civs to try it:
Maybe they work better, but you will need more cities as you will only get 2 faith buildings.
Poland: will get the policies faster (although only 2 as you want to avoid renaissance).
Maya; will get more faith and science with the pyramid, rush to Theology and you'll get a writer, artist, musician and engineer for a helpful wonder.
Egypt: much more happiness with the Tomb.
Ethiopia: Faster pantheon and religion, more faith, Stele is awesome.
Brazil: If you manage to get a golden age on the right time... meh
Policies:
Liberty -> Republic -> Collective Rule -> Piety -> Organized Religion -> Mandate of Heaven -> Religious Tolerance -> Reformation -> Citizenchip (Your workers will build roads really fast) -> Meritocracy (Huge happiness if you connected your cities) -> Representation (With Liberty completion get a Musician and send him to the civ you lack more tourism). You should win then but fill Aesthetics if you need more turns.
Tech order:
Pottery > mining > masonry > animal husbandry (then depending on your needs: bronze working / calendar / sailing) > archery > writing > philosophy (build temples in all your cities) > (if you have horses/ivory trapping to build circus) > wheel > construction > drama (build writer guild) > guilds (build artist guild) > Civil Service (buy open borders) > optics if you have coastal cities > education. Skip renaissance at all costs as it will increase your faith buildings cost a lot.
You don't need more techs other Civil Service to get Open borders and pikemen and machinery to get some xbows so you can even skip education and universities. You can go aesthetics or printing press to get some wonders but I don't think entering renaissance is worth it. In my game I entered at the last part and won before getting something in excchange.
Capitol build order:
Grow to size 3 then focus production: scout -> monument -> shrine -> worker -> pyramids (chop forests)-> settler spam (mixed with archers once you have archery). Once you have philo-> temple -> oracle > settler spam. When you stop settler production due to happiness build granary > library > NC > market > colosseum/circus > University.
City placements:
Send your settlers to places with tiles from your pantheon first and get a worker there fast. Then to luxes you don't have and later fill the gaps. At the end just send settlers to every spot avaible. At the beggining try to stay at positive happiness so you can grow some of your cities so stop settler production as needed. Later as your faith and tourism production is not modified by happiness just spam more cities.
Workers:
Steal a CS worker around T25+ and with those 4 workers with Pyramids bonus you'll be ok. Later once you have 6+ cities build 2 more to finish improving tiles and start roads once your capital is size 5+ and your cities 3+. With your workers prioritize luxes>strategics>chop>mines. You won't need farms until much later once you have enough faith buildings or meritocracy with your cities connected with roads.
Cities build order:
Shrine > monument > temple > granary > library > colosseum/circus > market > university. Focus production until the temple is built even staying at size 1 working a hill.
Select two cities with good food and production (with river for the garden if able) and build there writer and artist guild asap and fill their slots.
Gpt and trade:
Once pyramids are up and you start spamming settlers and archers you can go negative gpt, don't panic, once you sell all your iron, horses and duplicated luxes plus barb camps cleared, CS meetings and some trade routes you'll be ok. If an AI has a duplicated lux exchange lux per lux as you will need the happiness.
Your trade routes should go make gpt at the begginning and later to send food your capital and the cities with writer/artist guild. Once your tourism starts rolling 20+ send them all to different Civs to increase your tourism rate. Change base locations or disband caravans and get cargo ships as needed to get all possible different civs.
Religion
Pantheon: Scout fast your surrounding with the warrior and the scout to get a good idea but always get a faith producing pantheon, in this case I got stone circles but pearls or desert folklore one would also served. Prioritize in all your cities faith tiles always.
Founder belief: Church property> Initiation Rites> Tithe. If you have lots of lux tiles and a faith pantheon related to them like Religious Idols or Goddess of Festivals you can go with Pilgrimage but monument+shrine+temple+granary+library means -6 gpt per city so it's up to you.
Enhance your religion ASAP and then get a missionary to start your religion rolling. If you got Religious texts maybe your religion expands by itself and you can skip it.
Follower belief: 3 religious buildings, I got pagodas, mosques and cathedrals, if one is missing get monasterys, in case you fail to get 3 pick asceticism and spam more cities.
Enhancer belief:
Religious texts > Itinerant Preaches > Relicary. All faith must go to buildings so skip buying missionaris.
Reformation belief:
Sacred Sites. If you fail to get it just play a normal game, you're screwed.
Faith building buy order:
Mosques / Pagodas depending on your happiness needs > Cathedrals
Diplomacy
Buy open borders ASAP to increase your tourism rate and as said send them trade routes (specially to those with more culture output).
Once someone reaches renaissance send your spy as diplomat to whe most difficult civ (more culture output, no trade routes).
Try to avoid to plant your cities next to Civs with good culture output so they don't get mad and close borders or even attack you as it ruins your tourism output.
Build as many units as your gpt allows it and upgrade them, you want your neighbours to fear you and be peaceful as you will be "founding cities too aggressively".
Now some screens to ilustrate:
General view (My army is around Nicomeda controlling the Zulu menace in case you wonder)
Spoiler :
Game details
Spoiler :
Influence (finished sending a musician to Shoshone)
Spoiler :
My religion
Spoiler :
Policies
Spoiler :
I hope you like it!
