The last major landmass to be settled I believe is Madagascar, only settled ~1500 years ago, with only scattered, remote islands remaining unsettled past that point. Madagascar itself is an island, albeit one of the largest in the world, so enough to constitute 'major landmass' in my book; discount all island groups entirely, and the unsettled lands haven't existed for over 10,000 years.
What that means is that all of the "run[ning] away" you are talking about is still violently displacing native peoples. So for example, when the Boers flee the Cape Colony to the Transvaal, they aren't moving to virgin, empty land, but rather land inhabited by native Africans (Zulu, I think), who needed to be dispossessed of their land. And such dispossession tends to require violence.
