This is probably easiest in the Arks scenario (as you don't get any more people), but it can be done anywhere (in theory).
Place a few workshops and research Charcoal Kilns as fast as you can (Tier 1 in the Resources category), then be sure not to build anything else that provides Coal.
I don't think Gathering Posts count against the achievement, but feel free to test it. 99% sure they don't though.