Without force everything is voluntary, private property doesn't cease to exist as long as people have honor and abide by their word. It seems any reasonable system of people upholding their contracts would eventually result in private property?
From a purely anarchistic point of view, European settlers were within their rights to settle upon and use that unowned land. They weren't, however, within their rights to to use that "unowned" land at the expense of other people already using that land, and thus the Native Americans were within their rights to defend against such a deprivation of access. Unfortunately, the Europeans had numbers, guns, and smallpox on their side, and as the Native Americans retreated further West the Europeans continued to spread.
And to be clear: the Native Americans were using that land. A reasonably-healthy wilderness ecosystem is crucial for hunting, as any hunter can attest even in the modern-day; kinda hard to hunt bison if there ain't any bison.