HUMANKIND

There are plenty of routes for getting this achievement, to be sure, so I'll just document what I did.

I got this by playing on Metropolis difficulty, Quick Speed (it happened to be against three AIs, so not too many). If you dawdle during the Paleolithic Era, all of your rivals will advance pretty quickly to the Ancient Era. During this time, aggressively emphasize gathering food and influence, splitting your hunting parties until you have a bunch of scouts. Make a point of settling a large number of outposts in the vicinity of each other. (It seems like you expend less influence founding outposts in the Neolithic Era than once you are a civilization.) I advanced from Neolithic to Ancient by Turn 10, although of course YMMV.

When you advance into the Ancient Era, expand aggressively. Found two cities right away and attach surrounding territories to your outposts. In the City Management policy menu (select city, , ), switch your cities to emphasize City Growth. You also can dissolve a hunting party or two into your cities in order instantly to boost population. This will provide a boost to Industry, which in turn will help you build Influence-generating buildings and quarters and farmer's quarters (working simultaneously towards the aesthete, builder, agrarian, and merchant stars). As you get influence, use your remaining armies to continue to claim and incorporate territories as aggressively as you can manage (working towards the Expansionist star). In my case I was in a position to advance from Ancient to Classical by Turn 22.

Advance immediately upon getting your necessary seven stars; the advancement will as always occur the following turn. If one of your rival civilizations is advancing the same turn you will still get the achievement.