Answer: Every initial property rights claim involves seizure of property, in a sense. As no property rights exist before property rights are founded, there can be no endless chain of clear-title property rights conveyance.
It is a lamentable but unavoidable fact that before societies understood well and enforced property rights, people still used land, water, game, and other resources. Often, this leads people to overuse resources or into conflict. We can see this even today in the case of resources for which property rights remain unclear: most ocean fisheries, for example, many of which are already overfished. In the case of Native North American cultures, many were to a substantial degree hunter-gatherers and land was often held in common. Indeed, on Indian Reservations even today, much land is held in common (as in the case of the Red Lake Reservation in Minnesota that was much in the news recently).
Thus, in large degree, the colonists and later the U.S. government applied property rights to much of the continent for the first time. To be sure, this involved forcible expulsion of competing claimants to individual properties. But then, we must not forget that government exists to control the use of force, and uses force (ideally only in prevention or retaliation) to achieve its ends. That is why it is a uniquely dangerous yet necessary institution. Wherever it takes place, the first clear enforcement of property rights must involve the use of force against all who fail to comply.
Thus there is no reason to presume that property in North America traces back to some injustice. Indeed, the basic story is of people who wanted property rights to make hugely productive use of the land, and who instituted a government to ensure those rights and enable that productivity, and all the bountiful consequences thereof.
As a matter of law, the only property claims that are dubious are those that derive from land seized in violation of properly ratified U.S. treaties with Native American governments (i.e. tribes). Some property may be in doubt for this reason, but this is a matter of particular cases and following through on U.S. law.
This is not to say there were not injustices; there were. Andrew Jackson's dispossession of the Cherokee comes to mind as one case. And the tale is not a mere morality play: European colonists knew how to act under property rights most often because this was simply part of the culture they grew up in. Native Americans did not have a cultural tradition that supported property rights as well, and then those who did master the new ways often faced racism and other tribalist injustices.