In chapter 122, we learnt how Ymir got her Titan power. But still, it was only her power ( and then the royal family's power ) . How did it become the ability of the whole eldian people?
Before ymir frits got the power they were normal people. Then after ymir had children. Thus began the generation's of Subjects of ymir. Only they can change it to titans. To expand it they made other people bear that children. This is explained in the beginning of the season 4 part 1. Even if a Marleyen and an eldian have children the child will be eldian
Her descendants started raping as many people as they could and making sure those children did the same thing, until the families were eldians as well. They probably also killed the people they raped or imprisoned them.