It happens. E.g. the Inuit traditional diet is effectively entirely meat/animal products. Non-animal products make up a tiny sliver of the traditional diet.
Yeah no thanks, the Inuit lifestyle does not seem healthy. The Inuit currently have lifespans that are about 13 years less than the average Canadian lifespan. Even that is an improvement of 29 years from the 1940s. [0]
I have no particular take on the health of the Inuit diet; I bring it up mainly to indicate that there are people who do go essentially their whole lives on just a meat diet.
However your statistics there have way too many confounding factors to attribute anything substantial to the native diet. Infant mortality rates historically and remain (comparatively) very high. Alcoholism is rampant among Canadian indigenous people. Even among peoples who have similar diets such as e.g. Metis, Inuit and First Nations peoples, life expectancy is significantly different (this is before even getting into a comparison with other meat-eating cultures in the world).
There is virtually no signal here to determine the healthiness of an Inuit-style diet either way.
[0] https://www150.statcan.gc.ca/n1/pub/82-003-x/2008001/article...