More easy. Rush Horse Riding and attack with an army, after every victory you unit will reheal, then strike again. If you have Blitz you been blessed
This is much more reliable and lasts until they get rifleman, especially if you augment with catapults. After they get rifleman, you should have knights and cannons by then.
Land is key to winning. This means two things.
1) Expand your borders.
2) Stop your enemy from expanding.
Since Aztecs are one of the best early military civ, you should have no trouble stopping enemies from moving far from their capital. Plant one or two Warrior or Horseman close to their capital and kill anything that moves. Then settle right outside their capital or take over their smaller city, which should also be close to their capital anyway. Make that city a unit factory. Continue to put pressure on their capital until they can defend no more. Then move on to other civs, but with stronger units, until you have conquered the first continent.
Generally AI capitals are in good locations and by the time you capture them, their population matches your capital or better, especially if it once belonged to a scientific or cultural civ. Temple is almost always the first building you build in a capital (or any new city, really), now that it boosts science in addition to being necessary for cultural victory. Of course, culture also means Great People. Late game the 50% gold is the best trait for the last victory path if you decide not to pursue the other victories. Moreover, it can also fuel the other victory conditions by just spending it on units and buildings you need. There is no need to worry about the remaining civs attacking you, since Aztecs also excel in defense: cheap roads plus auto-healing is very hard to penetrate. In short, you get some great cities and any victory path is possible from here.