I’ve read the tribes require more than that. I don’t think you can join after discovering your ancestry. I think you need a connection to the tribe and traditions.
What are tribal membership requirements?
Tribal enrollment criteria are set forth in tribal constitutions, articles of incorporation or ordinances. The criterion varies from tribe to tribe, so uniform membership requirements do not exist.
Two common requirements for membership are lineal decendency from someone named on the tribe’s base roll or relationship to a tribal member who descended from someone named on the base roll. (A “base roll” is the original list of members as designated in a tribal constitution or other document specifying enrollment criteria.) Other conditions such as tribal blood quantum, tribal residency, or continued contact with the tribe are common.
from:
https://www.doi.gov/tribes/enrollment
This pop-up plagued page has more information I didn’t try hard to read:
https://www.powwows.com/much-percentage-native-american-enroll-tribe/
There are lots of variations.