Question

What Native American group was the first of the modern Native American tribes to live in Oklahoma

Answer 1

As near as I can tell it was the Chaktaw who were moved (forcibly) from Mississippi to Oklahoma in 1830.

Very soon after the eastern Shawnee were moved from Ohio to Oklahoma in 1831. Very soon after or during that time the Seneca-Cayuga Tribe of Oklahoma were also moved from Ohio to Oklahoma. You could look up the trail of tears to get the real story of how these moves took place.