Yoursheepy on steam and wiki said:
It seems to be a combination of all these factors, but mostly your territory and level (you need to fight for every territory, so they come together).
In my rush playthrough at normal difficulty, where I claim as much land as fast as possible, I got Chiefs in early June. By that time I got 42 territories and since I melee off every enemies, my soldiers are at pretty high levels (highest 17, total 132). I am also seeing multiple spider drones whenever I fight robots.
When capturing expedition solider I faced 25 enemies - 3 teams of 4, 2 teams of 6, plus the target. Most are armoured, including the solider I need to capture. I honestly suspect it cannot get tougher.
Time is 17th June, 46 territories, max lv 18, total 144. Expedition has 4 territories.
The first green matriarch, armed with martian cannon, appeared on 25th June, 59 days since game start. I claims 60 territories, my highest solider is lv 21, total solider lv 181, and the beastman has 5 or less territories (likely 3 or 4).
Martian capture mission, 4th July, 16 Martians, 1 Mech, 3 pets, plus the target. Martian has 2 lands and I have 69. Highest lv 22, total 217.
Then the shaman capture, 5th July. I meet four green matriarch, one red matriarch, two green captains, two chiefs, three rollers, six lower level units, plus the shaman. 70 territories, highest lv 22, total lv 228, 4 lands left for beastman.
This is a much, much faster pace then any Youtube video I watched. (I can go faster but I'm trying to fill in the wiki by experimenting)
If more people else can note when they first see the green matriarch, and soldier level and number of territories of both sides at that time, we should be able to do some calculations.
And I will add more of my observation data later. Note that I think Sheepy use soldier level, not adding tech and scien.
SO at 1st incident where I suspect 1st alchemist appear, since I overuse TNT in many mission and havent dissect beastmen yet so I cant see in mission its role, and corpse at the end only show soldier, and this mission show a beastmen healing device.
total soldier level 93 of 15 soldier (discounting Tab's 5) averaging 6.64 (discounting Tab's 6.12). Highest Harald 12
Total mission: 14/14
Total territory: 20
(total all class level 230, 23 personel)
A suspicion that average level 6 7 8 9 10 and territory 20 30 40 50 is the trigger. We will see when I get to said number.
Meeting 1st mech in a robot mission
Total soldier 110 averaging 7.33 (or with Tab 7.18) highest harald still 12
total mission 19/19
(total all class 244/23)
Since then I see the 1st levitating as well but havent got its wrecks.
Meeting a full court press: alchemist, captain, shaman, in a hyperspace gate mission. Although it's in Cydonia, I got another newer gate mission half a world away. No tech to destroy gate yet. (loot: 3 big rifle. 2 beastmen GL and etc...)
This time total soldier 121 averaging 8.648 (14 soldiers, I miscount two other times) or with Tab 8.4. highest harald = diego 13.
total mission 22/22
(all class 297/23)
just discovered Domes, building one, and get the second lab running along nicely.At this stage the Beastmen outgun me completely, as I only has rifle and TNT. Even ret laser is out of charge and cant barter for more.
My suspicion change to discovered territory number, not owned ones. plus level average.