During the Neolithic shift from a hunter-gatherer society to an agricultural one, humans started permanently settling and claiming land. But I presume that early on in the process, large amounts of land remained available for settlement. As time went by, the availability of free land decreased. At least by the time of the late Roman Republic, centralization of land in the hands of a few rich landowners became a structural problem for Roman society, as the poor were left landless and flooded the city of Rome. Julius Caesar ended up settling his veterans in very far-off lands that he conquered, which implies many men would be willing to permanently settle overseas, where they could get a plot of land, rather than in their own country, where they couldn't.
Since the Neolithic Revolution, in Europe (or contemporary societies that practiced agriculture, rather than continued living a nomadic or hunter-gatherer lifestyle), what's generally the latest point in which someone could go and freely settle unoccupied fertile land, uncontested?
a large part of the medieval era was devoted to "internal colonisation". clearing ancient forests and settling these areas, mostly by german settlers. that's why places like transylvania had such large saxon (german) populations up until the 20th century, lending an alternative name for transylvania - siebenburgen (after the seven fortified saxon mining towns). after the middle ages internal colonisation was mostly focused on areas that had been depopulated by war (the wildlands of eastern ukraine and crimea and the banat area for example in the 18/19th century). these migrations however were not something people did at their will, they were organised and even subsidized by the state. there was also plenty of internal resettlement after ww2 into areas that used to have a large german population (the sudetenland and western poland) but as these were mostly forced by the communist regime they don't really suit the criteria)