Of course there are couple of good candidates.
The Mixtec with Lord Eight Deer, his reign was from 18 of June 1097 till 10 November 1115.
Purépecha, Tariácuri (1350–1390), he is the founder of the Tzintzuntzan empire, I would recommend to listen to this podcast.
Other option is Tzitzipandáquare (1454–1479) the leader who fought two wars against the Aztecs (the Aztec emperor was Axayacatl.)
Iroquois with Hiawatha and the Great Law of Peace (pre 1451)
Chimor, Minchançaman (1450–1470) brought the empire to its maximum extent until the Inca invaded.
And there is my old Mississippian campaign idea about Cahokia from 1050 till 1190s. (control + f and search for What about the campaign!)
Also the Maya campaign would very likely not have any Europeans (but it could if you want!).
Pakal the Great would have probably the largest name recognition. Hunac Ceel is also a good option. If we want to have about Tikal and Calakmul rivalry then Jasaw Chan Kʼawiil I could be a good option. Or Yikʼin Chan Kʼawiil.
And then there are a lot of Historic Battle potential, if someone want I can also post those suggestions as well.