Great wall not possible on Earth 18. Ai always beat you to it
On immortal it is absolutely possible to snag Great Wall before Louis or Qin when playing as the Aztecs. It's usually my go-to way to play them on this map, trying for GW + Stonehenge combo, choke Rosie/steal Workers and settle out huge amount of land....but getting SH requires a LOT of luck as Louis gets it like 80% of the time if he doesn't tech Fishing first and Hatty is also very likely to get it if he doesn't. Shouldn't really be much different for an AW game as you are generally isolated as the Aztecs until 800-100AD anyway unless Mansa or Liza bolt to South America early.
Where are you settling cap? On the plains hill 2 north? Settling capital on the stone is not great. I use second city for this. Plus my start involves building warriors to rush Washington. So adding 1 element removes another.
There's no need to rush him though. His only metal is North of the cap which you can entirely control with choke on the hill next to it. He never settles for the copper even further North first, always goes West for Marble. Choking him will ensure he only has archers waiting in a size 6 city for like 100t. And you have a silver + nearby gold mine to support a few extra units.
Typical non-AW path is :
Settle 2N on PH, build one warrior to send to Washington to steal worker off Deer or farm to the SW of it, immediately build settler to settle on stone which just 1pops SH. Tech path Agriculture>Masonry>Wheel>Mining>BW. Build Great Wall in cap with natural hammers, stone city is only if you want to try for SH + Mids.
Always war throws a bit of a hiccup in here as you are not gonna steal a worker from Washington's Deer tile if you are at war with him. Great Wall should still be plenty doable if you go Warrior> Worker and settle in same spot though, just have to nix the stone settle which is for trying to get henge anyway (you build GW in cap and SH 1pop in the second city, 12t build, Stone only comes online for the last 4t of GW if you do things perfectly IIRC as you have to build the roads).
Get a pair of warriors on his forest hill across the river NW of Washington. Should get a couple more out before Masonry comes in.
Then build GW while heading towards BW.
When GW is done you can build settler for the stone spot to still try for Mids by T60ish completion date.
So the tech path only changes to put Wheel after BW instead, stone gets hooked up shortly after starting mids.
Add more warriors to the choke after barracks, then just prep to kill him (settle copper, roads and such)
Choke Rosie with like 4 AGG Warriors from a barracks city and you can ignore him until you take copper for axes to kill him off. I usually settle the copper+gold to the NW as my 3rd city for this purpose.
Just tested it a little and he only built ~6 archers with about 8 warriors, with more of each as roamers. Got the GW on t41or t42, Mids at 60 or 61, (SH was gone by t38, no chance without worker steal) choking him with 5 warriors and eventually an archer after I got Archery myself to garrison a forward city by the Deer+Fish to the NE for cottages moving forward. Pull back to get him to scatter units around 2-3 turns before your stack moves in, kill stragglers and move in on the cap. Overbuilt axes, final attack stack was 8 axes + 5 warriors + archer (w/3 more axes coming, killed the archers with axes first turn and wiped the city on the second turn, dead by t101 with 5 cities + mids and GW. A little bit more playing shows Currency date would still be around 125-130 not too bad for getting mids too and perfectly fine in Iso.
It's also completely possible to pants him with 3-4 AGG barracks warriors with only 2 in his cap by holding off on meeting him for as long as possible (t30ish), I've even found him with only 1 before because he likes to roam the others a lot. But this pretty much gives up GW unless the AIs are being dumb.