This can be done on a tiny map, and I chose a single computer opponent and 5 city states with barbarians also selected and played as Alexander.
Build your capital near stone which has a flat zone next to it (to allow the Stonehenge wonder to be built when it's available), build a scout and get it exploring to locate the barbarians, and a couple of slingers for defence, then concentrate on building a holy site.
Make sure you select the warrior monk option when you are able to create your belief. When you get enough faith to create the monk unit send them to the located barbarian camp. Hopefully you will encounter a few enemy units to get a promotion on the way. I then stayed close to the camp and destroyed the units as they were each spawned, but left the camp intact. Once a few more are taken care of you should have another promotion.
By this time your computer opponent should have a few cities which hopefully include 2 or 3 low population, un-walled ones. Declare war and attack each of these in turn. I was able to conquer a 1 and 3 sized cities, that had no walls, just with a single warrior monk unit that had 2 promotions.
You will need to build up your army as the other city states might have declared war, so do this as required. I had a few crossbows, melee and catapults available and attacked their units then lay siege to the city. By this time your warrior monk is formidable so just make sure you heal it if the health gets low but it's pretty straight forward to get them up to 4 promotions. If needed just make sure the monk unit is used to conquer the city.