There are 6 major matrillineal cultures today in the present world. That's already a sufficient disruption to any rule of 'universal' male supremacy in my mind. All of those cultures believe in balance between the genders and share power. This was and is also a common feature of many Native American tribes.

"The Six Nation Haudenosaunee Confederacy had, and still have today, a family/governmental structure based on female authority. Haudenosaunee women controlled the economy in their nations through their responsibilities for growing and distributing the food. They had the final authority over land transfers and decisions about engaging in war. Children came through the mother’s line, not the father’s, and if the parents separated, the children stayed with their mother, and if she died, with her clan family. Women controlled their own property and belongings, as did the children. Political power was shared equally among everyone in the Nation, with decisions made by consensus in this pure democracy, the oldest continuing one in the world."

https://www.nps.gov/articles/000/how-native-american-women-inspired-the-women-s-rights-movement.htm

I could go on and on building on top of all the evidence that Katie has already given because there is a slew of it, but I'm going to save it for a story, rather than spend more time here.