That's not really true. The Tribes had some pretty effective fisheries that did affect escapement. Indigenous peoples had some significant imapcts on existing resources.

Polynesians caused more extinctions of birds in Hawaii than did Europeans. Throughout the tropical Pacific they caused significant extinctions.

The megafauna in North America disappeared after the arrival of humans. While climate change was certainly involved, it wasn't the only cause.

There is some literature that suggests that the abundance of fish and game seen in western NA in the early 1800s and beyond was aided by the fact that smallpox arrived ahead of them.

It's not Indians, it's not Euroamericans, it is simply human greed and an unwillingness to control ourselves.