Your instincts are pretty much right already. Gonna assume you want to do it trad style
Writing -> Currency takes about the same time as -> Currency, so... yeah, dead on there.
The rest is an exercise in maxing your production by X turn; all the pop you can get and a set of mines etc on standby, so lots of early workers ... build/buy/steal.
Production; scout -> worker -> scout (if...) -> granary -> caravan (if...) -> library -> watermill/stoneworks/stable (if...) -> (all the archers you can make up to currency) -> !Petra!
The hard part is making it stick after that; settlers to play catch up on expansion or NC to play catch up on tech? Did you have enough luxes/gold luck to upgrade to CB's and buy a settler?
Tech: pottery -> (1-3 lux/worker) -> writing -> currency -> construction (so you have any chance of keeping it) -> philosophy
SP: -> Landed Elite -> (Monarchy if you can do it without delaying Aristo or if you need it for the happy) -> Aristocracy
One weird bit is stone/marble starts. With enough in a start, it can go either way on masonry before or after currency. I've had the math go both ways. Sometimes, buying a stoneworks can be a tipping point.
Even done perfect on a great start, you have to just accept that you may not get it regardless. Another point of failure is, well, lets see.... you have a good start (covet lands), a pretty wonder (covet wonder), and a weak army, so do not be surprised if you get DoW'd within a few turns of finishing it.
Good luck,
Copper