Going straight for Horse Riding as Scythia is already solid, as she usually has plenty of horse resources in the vicinity of her spawn. Dont spam military units from your capital right away, throw out a slinger or 2, or a slinger and a warrior. I usually play Epic but Ive tried marathon and I know it forces you to get a bit more military before settling your 2nd city because of barbs mostly. Sometimes an aggresive ai that got lucky with starting position or tribal huts and such.
Dont worry too much about improving your cap and get your 2nd city asap. If you can get a 3rd one right away better yet. Now is the time to start spamming military. If you already got the prod bonus for cavalry units and unlocked horses, go for it. Build 2 for example, and with her ability you got 4 horses. If not yet, build 3-4 archers (or upgrade your slingers)
Any non walled city will fall under the hoofs of your cavalry fairly quickly. Just beware of spearmen/pikemen and use your ranged units to disable them. If a city is with spearman or naval garrison, your horses will take a serious beating and you will lose a lot of momentum. If its a ranged unit or a warrior you can throw the horses in right away.
Also try coordinating your attack. Dont throw units into close range one by one. Take 5 turns or more if you need to position your troops around your target, so you can get them all in in a single turn and do more dmg + receive less dmg overall.
The only exception to this if the city is freshly settled and has no garrison, or you are bringing an especially powerful unit, you can take that pretty much effortless. Like, check the predicted dmg and if it indicates you will inflict 1/4-1/3 of the cities health in a single hit, go for it. Bring another unit just in case ai buys or build a unit to defend, and you can split your attack and capture 2-3 cities in the span of 5 turns.
In order to keep momentum going, the turn you are going to capture the city, pillage all the farms you can with your low health units, take the city with the unit closest to a promotion, so that it can be full health again in a couple turns. Keep some pocket change available for a battering ram buyout, in case they are walling their other cities, or start building one while you are out at war so that it will be ready and on location for when you reach the walled city (or if they happen to build walls while under siege)
Other than that its a bit like playing chess. I assume you are putting the cities under siege, yes? (they show a red heart icon in the city name = they cant heal back inflicted dmg)
Im not commenting about secret societies and heroes but, I think the most powerful combo for early war is Vampires + the Mayan twins Hunahpu & Ixbalanque. The vampire is virtually immortal, and the twins will steal defeated units (which can move and attack after you defeated them), so you can nuke units and multiply your army faster than you could produce it, while reducing your enemies numbers, very satisfying, and more powerful the slower speed you play.
Oh and remember to use Amani "agressively". If theres a nearby CS that ai is suzerain of, or pretty closeby, but you are 2 envoy away from suzerain, drop her there and "use" their units as extra forces. Just be careful not to let them conquer a city, as they will raze it. Be sure to keep a couple melee units to guarantee that the last hit on the city is yours. You can also throw a couple more envoys if you got some available to secure the alliance for as long as the war lasts and levy. You can do it without spending more envoys, but its very risky as they usually keep some spares, and if you lose suzerain, you lose control of the units and the CS will not help you anymore.