Had a bit of a try at how to do an opening sequence. Just so you know, something like this is possible after just 19 moves:
Three cities! Being IMP chopping settlers is rather strong. So went straight chopping after the initial slavery switch on T0 and if we have 4 forests in the BFC you can do this. Basically two chops per settler. First one came out on T9 IIRC.
However, there are downsides too of course. All cities still at size 1, slider down to 40% already, forests spent pre-mathboost. Still, I think chopping out 1 settler immediately is quite strong. It all really depends on what kind of land we have around us. Chopping settler+worker might work well.
Some by-thoughts to this approach:
1) Ideally the worker starts chopping asap. We won't know where to settle yet, but if we settle T1,
ideally the worker would already be on a forest in the inner ring of the city as border pop comes after first chop and chopping outside your borders gives less hammers.
This in turn means we should move archer and scout first. And then possibly stop worker move after 1NW as subsequent 1W (or even SW) is a guaranteed forest...
2) The archer shouldn't wander off too far away. I had my first chopped settler run into a lion already! Not sure when animals appear, but it's probably around T5, which IIRC is the case on ancient starts as well.
3) Note that if the capital is coastal and city 2 as well, we'd have immediate TR connection (as we have sailing). For the connection the (water)route should be completely unfogged, but not necessarily completely within our cultural borders.
4) A bit of a funny option, but settling on banana is an option for even faster settlers... Long term probably not the best thing, but if we move capital anyway, at least worth a moment of thought (before discarding

).
On a completely other note, I looked up what a "Quartermaster" actually is (for the non-natives

). On wiki it says "In land armies, especially US units, a quartermaster is either an individual soldier or a unit who specializes in distributing supplies and provisions to troops." which leads me to think that the Maze-type map astre mentioned may indeed well be the case... Nice long supply lines to our final target...