When I found my 1st city, after exploring the territories close to my starting position, transitioning from Neolithic to Ancient,  (approx. between turns 5 to 13, on average on fast game speed - 150 turn game), depending on what goals I want to accomplish - I think that having the population requirement is the only must have.  Everything else is optional, where I may shoot for those hunting or science objectives too, if I feel close to achieving them, but not going beyond maybe 13 turns in trying to be a perfectionist.  Let's say, this is a normal game, so maybe around turn 9 or so.  Also, I will wait, if Idon't find a site that meets the following requirements, for planning.

Here are 5 key things I look at for my first site, and to keep in mind, initially. I don't always use the suggested tile for city placement.
1. Look to maximize industry resource at the founding cite, specifically inside the territory, while being next to 3 connected tiles that carry food. I like to try to found the city on woodland, and be next to mountains (if possible).
2. Sacrifice 2 scout units for population into the city immediately. Minimize sustainable food in FIMS, maximize industry FIMS, then second on Reseach, when those slots are full.
3. Pottery for an extra 4 influence/turn, so that Outposts can be claimed sooner, competively.
4. Use a 3 Farm development plan. (where the farms are adjecent to each other, (adjecency bonus) and each have a minimum of 2 food each). Easy w/ grassland. Better w/ rivers.
5. Research Domestication, build on the Horse Resource, and build Animal infastructure, magnifying the farming bonus.

Then, I will shoot to be out of the Ancient Era, between turns 21 to 34. (this is a ball-park estimate, depending if I qualify to get out immediately, or if I choose to be a star perfectionist. Mabe, in reality it's around turn 28 or so, where I reach an average decision. These numbers aren't exact. I'll attach territories too, but at some point that gets expensive, and I know I should do a city instead of attaching even more. I've had an attachment cost 240+ influence before, very early on, which is almost the same as a Wonder of the World. I wonder if there's a way to quickly activate the Civic that makes it cost money instead of influence. That would be cool.

Notes:
Militarist Stars seems to be the hardest for me to get. I know at some point in this growth model, I should be producing units and other upgrades, etc.
Science Stars seem easier to get than Money stars, but then should I value Money FIMS more than Science FIMS, or should I pick even a Merchant culture, early on? Some thoughts are Babylonians (Astronomy House), Olmecs (Head farm), and Assyrians (Dunno + movement speed) work well for this strategy (I think).

I am open to feedback, and hope to improve my game.  I mostly mess around at Hamlet difficulty, winning it, but I can improve.  Im far from an expert, at this point.  I consider my playstyle to be an agressive pacificist expansionist, early on too.  I'll found territorites on boders of other players territories, but then I'm not the one who decides if its a war.

Generally my game plan is to delay going into Ancient until I feel I have enough pops to just rush down and conquer at least one of my neighbors, so that time frame you quoted sounds about right, but then to intentionally rush through Ancient ASAP.  Getting into Classical 5-10 turns before the AI even starts thinking about it does two things- it ensures you have access to whatever abilities or Emblematic Units/Districts you want without competition, but it also gets the snowball rolling- if you go into Mauryans, for instance, you get *way* more influence per click than if you stuck around in the Ancient Era, or if you go into big industry it allows you to stack powerful emblematic makers quarters adjacent to each other giving you enormous resource advantages over the AI.  I think I'm still pushing too aggressively through the later eras, but given that Classical is just Ancient+ I've found that going through Ancient at a breakneck pace sets you up really well to eliminate some competition and get your empire set up to dominate in the mid/late game.