How can I unlock the 'Hour of Alpacas' achievement, given there hasn't been an event in years?

The 'Hour of the Alpacas' is a date/time-based achievement.

The idea being that every once in a while, Age of Mythology: Extended Edition's developers (Skybox Labs) will launch the 'Hour of the Alpacas' event. If you start a match during one of these events, the achievement will pop.

I personally dislike achievements like this - it's not a showcase of skill, or a prompt to complete a challenge a certain way, you just have to be lucky enough to be playing the game when the developers decide to activate the event. Which, ok fine... but the developers haven't launched an Alpacas event in about 5 years. As a bit of a closet completionist, stalking AOM and Skybox's Twitter accounts hoping for an event is wearing a bit thin.

Is there some other way to trigger this (mostly) pointless achievement?

While it won't be legitimately obtained, if you only care about ticking it off for completion's sake, you can unlock it by setting the your system clock/date back to the last-activated Alpaca event: 7th Feb, 2016. The achievement will trigger when you first load into a match (Singleplayer is fine).

1. Quit the game, if running.
2. Set your system clock. In Windows 10:
   • Right-click on the date/time on the taskbar and click 'Adjust date/time'
   • Turn off 'Adjust date/time automatically'
   • Under 'Set the date and time manually', click 'Change'
   • Adjust the date to 7th Feb, 2016. and click 'Change'
3. Launch the game
4. Start a quick single player match. The achievement should pop up.
5. Quit the game, and remember to change your clock back and re-enable automatic date

Similar to Robotnik's answer, this won't unlock the achievement legitimately but you can use Steam Achievement Manager to unlock it with a lot less effort.

I personally have used SAM before to unlock the "Yes, I am the real Garry!" achievement on GMOD. This achievement is in the same boat as yours, in that you can only be awarded it if you play in the same session as Garry (the game's creator). Well, Garry doesn't log in nowadays, so it's impossible to get the achievement legitimately.