Here's the setting that I'll play in:
-Single player game against comps
-Noble level
-Mayan Empire
-Small map
-Temperate climate with normal speed and sea level
Usually when the game starts out, there's at least one of the following terrain feature near your potential capital: coast, river, hills, heavily wooded region (not jungle). These terrains provide different kinds of benefit early on in the game that is crucial to jump starting ur civ:
-coast: normally, coasts provide +2 money, but as a Financial leader of Maya, you get an extra money, so you get total of +3 money for each coast tile. Also, upon researching sailing, coastal trading is enabled.
-river: like coast tiles, the tiles the river runs through gives them +1 money, and enables trading when you research "sailing", and it can also be used to connect ur cities or resources without building roads to connect them.
-hill: hills are only beneficial if you build a mine on it in the beginning. WRONG. if you build your city on the hill, you can utilize the hammer.
-wood tiles: obviously they provide you a way for cut-and-rush tactic, where you can cut wood to finish products.
With these basic terrain features in mind, let's try to jump start the civ. Keep in mind that depending on the situation, you may need to be flexible.
When the game starts, move the given warrior/scout first to see if you can pick a better location to spawn ur city. That doesn't mean you should roam around the map looking for a perfect spot. If you can find a better location within 1 movement of settler, do it. Perfect spot will have all four terrain feature described earlier.
Because this is a small map, there's likely to be 2~4 continents, with anywhere from 1~3 civ on each continent. If you are alone on your continent, you can be a little bit relaxed about spreading, but if not, beginning is the perfect time to eliminate your opponent to avoid future clashing of cultures. Because the continent is pretty small, sometimes you may be less than 10 tiles away from another civ.
If you did as I advised and built your city on a hill, you can churn out the first warrior within 8 turns. Of course this should be done while roaming to search your nearest opponent. If lucky, you will find one early enough. The computer most likely made another warrior to guard the city and a worker, so if you go in with two warriors, there's a good chance you can take over the city and eliminate your first opponent.
If one warrior arrived at the other civ first, make sure the other one arrives near the city so you can declare war with two warrior, instead of have them enter separately and get creamed.
Unless you're dealing with a special civ that starts off with Strength 10% bonus for its melee units, or is on a hill, the warrior guarding the city could have maximum strength of 3.8, as opposed to your both of your warriors 4.0 if you defeated a couple animals/barbarians on the way their, there's a chance that you leveled, and the smart thing to do in that situation is to get the 20% city attack bonus.
However, there's a chance that this may not work. To get some benefit out of attacking the person, try to enter the city and declare the war when there's a worker working at the edge of the civ's city. That way, even if you aren't able to capture the city, you will have captured a worker.
If you don't think you can take over the city, you can still stall your opponent by pillaging, and taking over the tiles. The tiles your units occupy cannot be utilized by your opponent, so you willy quickly see the city's pop. dwindling.
If you did all this, you should be ahead of your opponent. You may potentially have a city, a worker, or both.
Here's the tech tree that I try to follow in the beginning: Maya starts off with mining, so I only need to research bronze working to be able to cut down trees. As soon as this tech is available, I use it to cut-and-rush my stonehenge project. Each tree chopping period takes 4 turns (1 turn to move, 3 to cut), and yields about 20 hammers. Stonehenge costs 120 hammers, so you can usually build it after clearing about 3~4 wood tiles. This enables your cities to expand its border after 10 turns, which is crucial for securing your locations on the map in the beginning in order get resources.
If you captured the first city, the same process should be happening with the Oracle, so you can get a free tech. If not, but you have warriors left from the war, use one of them to secure a potential plot for the city, while your capital makes the settler. After that, your capital should make the oracle.
There's a lot more to this, but I'm getting sleepy. Important thing is to be flexible. One thing I want to emphasize is that building a capital on the hill really does help for a long time.