First of all, please recognize that the term "Native Americans" refers to members of a variety of cultures extending from the southern tip of South America to the Arctic rim. These cultures were and are incredibly diverse in their customs and practices. They range from city dwelling agriculturists to unspecialized hunters and gatherers. It is therefore clearly impossible to make generalizations about such an enormous and varied population.

I specialize in Pacific Northwest and Inter-mountain West groups (from NW California to southern Alaska), so I can tell you a little about some of them. But even among these groups there is an enormous range of variability in celebrations and recognitions of life stage events. Also, practices may relate to social class so they may vary in that way. One thing they hold in common, is that there were none focused on an individual that occurred on an annual basis. So the answer in my area, to the best of my knowledge, about Birthdays is no.

Some examples of life events that were and are recognized in elaborate rituals and very strict conventions in the NW include: rites of puberty, celebrations of same (Hupa, Yurok, Karuk), time of naming (many, many groups in the NW had these), ear piercing of noble children (Tsimshian, Tlingit, and someother far North groups), assumption of the responsibilities of uncle (Matrilineal and Matrilocal groups of the far North), marriage (most groups), and time of death/burial (virtually everyone in the NW).

There were celebrations/ornate rituals that took place on an annual or biannual basis, but they did not focus on individuals and they were not related to life stages. Examples of these include the "world renewal ceremonies" of peoples in the south like the white deerskin dance and jump dance of far NW California.

P.E Goddard, 1903 Life and Culture of the Hupa

Richard Keeling, 1992 Cry For Luck: Sacred Song and Speech Among the Yurok, Hupa, and Karok Indians of Northwestern California

Jay Miller American Indians of the Pacific Northwest Collection

K. Ames and H. Maschner, 1999 Peoples of the Northwest Coast, their Archaeology and Prehistory.

W. Sturdevant, 1990 Handbook of North American Indians, Volume 7: Northwest Coast

Edit: formatting/grammar.