On a tiny map, to rush domination? You should have won by turn 150 more or less. Its actually easier than you would imagine. Build 2 or 3 cities, build an army, usually archers, with melee support and go to war. If you havent won or look like winning by turn 150 the super fast domination falters and you are into later warfare territory, and in fact will probably lose through inferior units and terrible science. The aim is to do a crossbow rush, more or less, but comp bows will get you 1 or 2 quick captures, usually.
Scout, scout, warrior and archers, build a settler on size 3 pop in capital. try to steal workers, ignore science and religion, keep pumping out units. On a tiny map anyway. On bigger maps there is a balance point where you may need to go libraries and NC. The odd granary sometimes as size matters in warfare also, for the unit cap.