The start isn't as bad as it looks at first glance. Sure it's icy, but it has Marble (good for production and early wonders), deers (very good for trades!), and fur (a pre-calendar happiness resource!). Additionally, it's on a lake which will provide a good amount of commerce once we know Fishing, so in the beginning of the game we will have a good capital city. It's only later in the game that the capital will become bad, when the happiness limit would allow for a larger city and except lake tiles no good tiles will be available - but maybe we can move the palace then, we'll see.
This is an extreme adventure and supposedly very hard, so I have to leverage every advantage I have. This in our case means two things: Religion, and marble. The Aztecs start with Mysticism so they can found an early religion, and the availability of marble at the capital means I can build some early wonders that support the religion strategy. The only problem with this is the lack of commerce in the beginning, as I cannot work the lake until we knew Fishing. I decide to go for Meditation as my first tech anyway.
We knew Hunting already which is needed to improve the deer tiles, so I produced a worker immediately. Too bad that there's a mountain blocking access to the southern deer tile! Looks like I need to find a way around the lake to imrove it, or maybe build a galley later (on a Highlands map?!?). The scout is sent the only possible way right now, west, pops a hut, and gets a clone!
Nice. So both scouts move on, pop another hut...and get Animal Husbandry! That's even nicer. Meditation comes in in 3600BC, I found Buddhism, and immediately convert. Research is set to Masonry next, to make use of the marble tile, then Priesthood to be able to build the oracle, one of the early wonders that get built faster if you have access to marble. One advantage of such an icy and resource-poor start is that I can afford to skip all the early worker techs for now, like Agriculture or Pottery. You have to see the good things in everything to enjoy life! More huts get popped, and I receive experience, gold, and more gold. I also get a warrior from a hut, but he's immediately killed by bears...and in 3000BC, a hut yields another tech, Archery! A few turns later, yet another hut nets me yet another tech: Agriculture! What's up with my luck with huts? It's insane!
Meanwhile, my capital had built two warriors after the worker, one to garrison my capital, the other to fortify at the choke point west of the capital. Immediately thereafter, I started to build an early wonder to get some great prophet points going, for an early shrine.
As you can see, I'm already making a deficit - with only one city! How did that happen? Well, I popped more huts, and got several warriors out of them. I had so many units roaming around the map now that I actually had to pay unit upkeep! That had never happened to me before that early in the game. But I had also received a lot of gold from huts to be able to afford this, and in fact liked to have so many scouting units. While I was popping huts like crazy and moved around the maze of the ridgelike mountains, I really wondered where the AIs were, though. The only one I had met so far was Caesar - where was the rest? I'd like to meet them as early as possible, to reduce tech research costs!
I found them, eventually. I met Mao in 2720BC, Saladin in 2480BC, Alexander in 2080BC, Victoria in 1560BC and Mansa in 850BC. After completing Stonehenge, I built a settler to found my second city in 1720BC, in a similarly sorry spot as Tenochtitlan was. Not that I had much choice!
As you can see, I had started building the oracle next, and completed it in 1440BC, taking the expensive Metal Casting as my free tech, seeing that silver would be available soon. I actually had to slow down production in Tenochtitlan for some turns to let my research on Bronze Working complete first. After Bronze Working and Metal Casting, I researched Sailing, then Writing for libraries, then Iron Working to see where iron was (I had no copper!), then Alphabet for trading. Meanwhile, my hut luck continued to be insanely good. In 925BC, I received Horseback Riding from a hut! Not that I needed it (I had no horses), but usually it makes for good trading material once Alphabet is known.
Both stonehenge and oracle generated great prophet points, and in 900BC the first one was born. He immediately built the Mahabodhi in Tenochtitlan. A few turns later, I founded my third city.
It was in a very crappy location that was even worse than those of my first two cities. It would only be able to grow to size 2 in the beginning (later, with windmills available, size 3 would be maximum), at least if I did not want to steal tiles from Teotihuacan. But it grabbed both silver (two happy faces with forges!) and another marble (which is great for trading!), and controlled the only land access to my other two cities. Additionally, it only built a lighthouse and a barracks, and provided my empire with military for a long time so that my other two cities could focus on more important things.
I finally discovered Alphabet in 450BC, and traded a bit during the next turns. I gave Meditation and Priesthood to Mansa for Polytheism, Alphabet to Greece for Mathematics, then Iron Working to Mansa for Monotheism. My own research went into Literature, for yet another wonder - the great library! Meanwhile Caesar, who you could call my "direct neighbour" because of the map layout, built the pyramids and adopted representation, probably giving him a nice boost to his growth curve. That was not good, considering that I most probably had to fight for better lands sooner or later, and he was the only one I could realistically reach via land...
I had sent out a jaguar west to guard a nice city spot with iron plus some other goodies...but came too late: The barbarians had already founded a city there.
I completed the great library in 50AD, and also made some more trades. I had researched Currency and Music (as the first in the world!) on my own, and now traded Metal Casting away to Alex for Construction, to Victoria for Calendar and some gold, and sold Polytheism to Rome for more gold. Mao got my extra deer for some silk, Mansa received Construction for gold as well, Saladin Mathematics for even more gold and now I had a tech lead and lots of gold to fund 100% research for some time to come.
Another great prophet was born in 75AD, and he founded Christianity - unfortunately in Tlatelolco, my mini-city. In 125AD, I completed the colossus to help with research even more - I had to use every advantage I could get with these lands! Talking about bad lands and how I had to leverage every advantage I had, I had built a galley and ferried a worker around that damned mountain at Tenochtitlan, to improve the last deer tile...
In fact, this galley would prove to be my most important unit for the whole game and one of the best decision I had made. As it turned out, we were situated north of a large lake with nice lands south of it. I could have spread westwards, but the lands there only hold a lot of tundra for me, and the distance to the capital would have been brutal. South of the barbarian iron city (which I intended to capture!), lands were better. But Rome was spreading there already, and I did not want to mess with their praetorians - yet. So I decided to use the galley to ferry my settlers over the lake, and found my cities around it. They would be nearer to my capital, full of lush, green lands and resources. The only problem was that defending them in case of war would be a nightmare, but I was willing to take that risk.
Somehow, this game reminds me a lot of Epic 12: The Gauntlet, back in Civ 3 days. It had been a game on Deity, in a similar icy situation. Only one player, Urugharak, managed to win that game, everybody else (including me) lost. One of his key moves had been to use the lake at the starting location to its full advantage, founding two cities in close proximity of the capital around it. I intended to do the same here, although the lake was a lot larger here.
In 540AD, Texcoco was founded. Grasslands! I actually had grasslands to work now, imagine that!
I defended my cities across the lake better than my core cities, but I didn't really fear war right now. Mao would be the only real danger to these cities, but he had converted to Buddhism already and was my friend now. My next city, Tlexcala, was founded at the copper west of Texcoco. I planned Tlex and Tex to become major beaker producers in the future. I now produced Buddhist missionaries as well to convert and befriend more civs. I would wage war eventually, but right now I needed more peace! Un 760AD, when I captured Bantu, the barbarian iron city, I had already managed to convert Rome, so my two neighbours were on good terms with me now.
I founded some more cities until 1080AD, at what time I felt I needed to stop building settlers for some time so I wouldn't overexpand. I could only afford 50% research rate right now, and no AI had any money I could get.
I was researching Education on my way to Liberalism at that point, and discovered it first in 1370AD. I took Nationalism as my free tech to build the Taj Mahal, and researched Rifling next. I planned to attack Rome! My lands were not good enough for a victory, that much was clear, so I had fight for better lands. Rome was reachable without too much pain, and had nice lands as well, plus Caesar was behind in tech, so he was the obvious choice. I planned to build my forbidden palace in his lands. Still, the war would be a logistical nightmare: Look at the mazes of mountains south of Bantu I had to cross with my units to reach him! But this would also mean that he would not be able to counter-attack me though, and I would be able to defend some strategical choke points nicely.
I got Rifling in 1580AD and shut down research for several turns to upgrade my city raider jaguars, then researched Military Tradition next (and founded another city east, near horses). Until now, the world hat been peaceful - too bad, because I would have liked for Caesar to spend his forces somewhere else before I attack. Hm...what I could do about that?