I dont know what your level is but just in case: first off, understand that if you play anything higher than Prince difficulty, your start is going to be slower than every other AI. In my games Im usually behind until T150-T180 and start generating more science/culture than turns have passed at around T220-250 depending on the civ in question and spawn/natural disaster rng. This is King difficulty on epic speed btw. I almost always go for science victories, but I hate not getting a religion, so I usually go like this:
Settle 3 cities, build 1 or 2 holy sites depending who is my neighbor and what they have done until that point. If I got a neighboring civ that is already rushing religion or spreading it to my cities, rush to get temples and apostles to first eradicate other religions from other holy cities.
While the first 2 apostles are on their way to spread my religion, I am finishing the Gov plaza+ancestral hall and sending out new settlers and starting to build the highest adjacency district that cities can build at the moment, either a campus or a commercial hub. If there is no really attractive spot without having to buy 2 tiles, keep it busy with some military unit, a builder or city center buildings until they grow
Especially helpful if I get a Debater apostle, spread to other cities and with the last charge remaining, wait by their holy sites and fight the missionaries when they get out to reconvert their cities. I have to wait a bit to get enough faith for a third apostle to evangelize and get the 4 beliefs, but its easier to spread to enemy lands that way, which helps next part of the plan.
As a religion spreader, I choose religious colonization 90% of the time. Spread fast to enemies, and every new city they found, has your religion already and starts building pressure. If my neighbor is sending lots of missionaries and converted a bunch of my cities already, I go for cheap religious units and the spread will have to be more micromanaged. Next, choose some belief that boosts whatever I am lacking at the time. Tithe if low on gold, +2 faith per city if low on faith, etc. Science or culture per 4 followers are especially powerful in this combo.
Other districts that come later I dont build right away unless theres a naturally good spot for it (like a +3/+4 IZ without aqueduct or dam). My first 2 coastal cities build either 1 military land unit if Im at war, expect one, or planning to go to one, or fighting barbs in the area. A galley if none of those apply, and then to harbor, because I dont settle coastal soon unless it has at least 1 sea resource in the vicinity to get a +3 harbor. This is for going for Mausoleum of Halicarnassus as soon as possible, so the coastal city that has better potential for that wonder will rush the harbor buildings. I will build an aqueduct as soon as possible too in a convenient spot for the boost, then Ill evaluate if the other cities really need them and build them when those cities cant build anything more interesting at the moment.
Theater squares I build in spots I get at least a +3 from adjacent districts and/or wonders, and pretty late game actually. I might have already built half a dozen industrial zones before I build a Theater square that really attracts me. I rarely build more than 1 or 2 actually. I only build more if I went on a murderous spree against unlikeable neighbors and Im managing like 30 cities @T200
This approach was usually working for me to get T360-385 Science victories (more war and cities captured = faster SV). Now with the corporations gamemode Im getting T280-330 culture victories depending on map size (bigger = slower), while my spacepors are working on some project and Im some turns away from SV
