Speaking as someone who tried to build just that in Crusader Kings 3 to great success, how would you propose we do that?
Surgically remove one boob so women can use bow & arrow more efficiently. Then, make them go to military school, and when they're 11, throw them in the middle of nowhere in Siberia with no food or water. If they return with the head of a Russian general, they are ready to integrate into the society.
It still raises a lot of questions though, like how they'll treat bastard children.
Crusader Kings 3-wise anyway it involved reforming an entire religion and set of cultural values for it to start showing gains. They basically captured men to use as Concubines who were little more than breeding mules. Considering in a Matriarchal society in CK3 normally you end up with super weak men (similarly to how women end up under Patriarchy) it ends up being more advantageous to play the game promiscuously, then to legitimize bastards as a way to gain claims on other people's lands, or to have children from captured kings and war generals to snag their stats under your own banner.
Aiming for a society where both of the sexes have complete equality means twice as many soldiers but also twice as many people who want to become Vassals; It tends to be easier to pick one gender to rule over the other and with women at the helm in CK3 you actually have advantages over other cultures when you play it within the right religious and cultural lines.
Here's my explanation for the build, for anyone who cares:
In order to empower this, for your custom religion you'll want the traits Carnal Exaltation to turn Lust into a Virtue and for the rise in fertility, Sacred Lies so that you gain Piety for gathering men's seed in secret and otherwise being seductive, and Polyamory so that when spotted you don't get in trouble for it... but the other participant from another culture does. If you want to play them as more of a warfaring Amazonian tribe you can replace Polyamory with Warmonger, or if you want to enforce these tenants in such a way as to ensure they remain you can adopt Legalism to have your followers embrace Lust and Deceit even more, or if you're really concerned about heirs you can take up the path that lets you turn them into monks so that they can't turn on you, allowing for powerful holy warriors with no claims on your property.
For the Doctrines it must be Female Dominated, Marriage must be over Consorts and Concubines for the Breeding Mule Program, there must be No Bastards so that they can have a claim within your culture on others' lands as claimants, Adultery must only be allowed by Women, and it can be played within pretty much any religious foundation. Allowing for Deviancy and Witchcraft is a plus, there's no minus to it in this model, so I went for it. It may also be advantageous to allow for Kinslaying if the populations start booming too quickly as to cull the weak from this culture.
Breed your line around the Fecund trait if you want a large collection of subjects, or if the same religion is played as through Men instead you can use the Sterility trait as a weapon upon other cultures through Carnal Exhaltation + Lust getting you over that hurdle before you've even hit Lifestyle Traits.
A female driven society can be quite successful, but a lot of ideas ingrained by masculinity from our history need to be undone to turn it into something more advantageous. By modeling off of Amazonians and Lilith they can actually do a surprising amount of damage over having two sexes worth of healthy breeding stock to work with instead of just the men being stronger, doing so through male concubines and legal promiscuity that you're expressly rewarded for doing.
Ę̵̚x̸͎̾i̴͚̽s̵̻͐t̷͐ͅe̷̯͠n̴̤̚t̵̻̅i̵͉̿a̴̮͊l̵͍̂ ̴̹̕D̵̤̀e̸͓͂t̵̢͂e̴͕̓c̸̗̄t̴̗̿ï̶̪v̷̲̍é̵͔
