Well, it's tricky. Even trickier with Tradition. You have to interrupt your build queue and stagnate to get a settler out. Without a great start location, this stall time can be a lot of additional turns.
Ideally you want a settler out before t40. If you put your settler on a hill *and* go liberty *and* work a 2food1hammer tile, you can knock out the monument in 10 turns. By then the city has grown and you go straight to library. t30 settler vs t40 settler makes all the difference here.
This is why the free settler from Liberty is so powerful. If you're spending t20-30 building a settler, you're *not* building archers.
However you do it, you want a city planted by t35 if possible, on a hill, with a 2food1hammer tile to work. You can't afford to rush-buy that library because you need the money for composite bow upgrades. You can't afford to skip the monument because you want to finish liberty.
And that's for 2-city NC. If you go for 3 cities, it's even trickier. However, with 3 or 4 city liberty, the turns you lose making settlers you get back from having 4 cities building archers.
There are a number of guides showing how to do all this juggling. Moriarte's liberty domination guide is one.
Rule #1: Never build workers. Steal them.
Rule #2: Settle on hills.
Rule #3: Settle on luxury mines, if possible.
You can sell your early resources to the AI for 7g/turn before you need the happiness. If you settle on a mine, and tech mining after archery, you can earn 300g this way by the time you attack. (2g/turn, 3 w/ gems for the tile, + 7/gturn from the trade)
If you do this with both your first and second city, you can hit 500 gold by the time you attack. (From this alone... 300-400g more from scout exploration) This buys 2 archers. (Or a library)
If this seems like excessive min-maxing... well that's Deity for ya.
Liberty:
Monument build time in a size 1 city on flatland: 20 turns
on a hill: 13 turns
working 1 2food1hammer tile: 10 turns
So, a size 1 liberty city on flatland builds a monument as fast as a tradition city on a hill.
Saving 10+ turns on monument build time in the early game will obviously influence how long it takes to build NC, and get archers out, etc. etc.
Now, if you open Tradition (and get a culture ruin) you can avoid building monuments entirely, but if you have to wait until t25, it's bad to skip building a monument. So you have to build that monument. With a 2-city NC, you're only getting one free monument out of the deal. That's 40 hammers. You earn that many extra hammers (base) in 20 turns on Liberty. (+5% while building libraries/NC)
In the long run for a peaceful game, even with no culture ruin, Tradition saves hammers by giving you 3 free monuments and 4 free aqueducts. (520 hammers)
This is a HUGE amount of free hammers, and in 4-city games it's roughly 60% more than you get from liberty by t100. (1/city/turn +5% is 100 from capital + 65 from expo 1 + 55 from expo 2 + 45 from expo 3 + 5% of 520 hammers (25) + 5% NC (6) + 5% Libraries (15) = 311 hammers from Liberty. In a 2-city game where you don't care about aqueducts and don't go past Monarchy, Liberty outperforms though. And turns saved early count for a lot.
Tradition *also* outperforms hammer-wise when you *want* growth. (Because more citizens = more production)
But, if you're not even taking Landed Elite, Tradition can't spit out monuments/libraries/settlers/archer/NC as fast.
This is not meant to say Tradition isn't as good. I'm just saying that if you want t65 NC in a warlike game, it's easier with Liberty. IMHO.
Not to derail, but this is one of my biggest complaints about Honor. Taking Liberty to boost production of archers feels broken. Honor should be better at building my army!!
Also, I don't mean to imply that you *must* hit t65 NC. I just think it's worth doing that at least once, just so you understand the sacrifices/tradeoffs involved. I think t85 is more reasonable benchmark for a successful domination run.