Not much to it really, I did it on the first try. Although I likely have luck to thank for that. I made the custom civs and set the map settings as follows. Just split up your initial force, settle your city and play it as if you were playing normally. Then, with your starting forces, try to find the AI army before they themselves settle. Once in battle, just clobber the settler and presto all done. Hope it works for you! Yes this is an ultimate cheese win, but it's a win without mods at least!

Step 1: Your Civ: This is what I used but anything with fast moving starting units is best, gotta find the enemy fast!
Big thanks to Zapp Brannigan for pointing out that the "Well Connected" trait can increase odds of winning substantially.

Step 2: Enemy Civ: Set to Cultist affinity then nerf 'em. Have you even SEEN the modifiers endless difficuty gives the AI!?!?! Screw that, make em as weak as possible, which is still stronger than normal.

Step 3: World setup: VERY important to set the world small, with one landmass, few obstructions, and close start to other empires.

Step 4: Split the starting force and spread out. The AI has a score of less than 20 until it settles and gets started, so if that score goes over you've likely missed out. I managed to catch them with only my hero and one of the 2 starting units. Used my starting unit to lockdown the enemy hero and used my own hero to shoot the settler twice and that was game. I guess the AI is much more picky with it's starting location with the Cultist affinity, the length of your attempts will depend on how good their start is I guess.

Big thanks to Falcon_BR for the tip!
After winning, play to turn 25 and you'll also receive two more archivements!
"Quick out of the Blocks" and "Fast Start"