I have another related question, what is the longest line of "nobles" / the societal equivalent that is directly traceable?

edit: found a related thread https://www.reddit.com/r/AskHistorians/comments/12lghm/whats_the_longest_traceable_historical_lineage/

There probably wasn't just one time and place that people decided on ownership of land. This was likely a process that happened all of the world independently and at different times for different reasons.

However, one model for how ownership is decided that fits the evidence pretty well for at least two parts of the world (and probably more) is a "first comers" model. In short, the idea of "first comer status" is that early agricultural communities decide land ownership in part through use rights. In other words, that whoever is using the land, and most importantly, who has been using the land for generations, has some claim on the ownership of that land.

This seems particularly true in southern Arizona were the first farmers north of Mexico started building agricultural communities around 1500BC. In these communities we usually see that the earliest homes are build around a central plaza, and that subsequent homes are built and rebuilt on top of those first residences for hundreds of years after. We also tend to see these homes get larger over time, and the largest homes in the village are typically adjacent to the plaza. The argument is that these people, as founders of the village, get to lay claim to the best agricultural land by virtue of having been the firs to settle there and also the people whose family has been farming that land for however many generations. Because they have this claim to the best agricultural lands, we see the beginnings of social differentiation (in the size of their homes compared to the average in the village). The symbolic act of building and rebuilding homes in the same place (at the center of the village) makes a social statement about how long your family has been there and so how your family has rights to particular farmland. This is the interpretation that Vint makes for Las Capas, and other Hohokam scholars have made similar arguments.

This same "first comer status" may have been applicable in parts of the Neolithic Near East. At some settlements in this region we really see evidence for ancestor worship cropping up at the same point in time as sedentary agricultural societies. For instance, the plastered skulls at Jericho. The idea being that making strong statements about who your ancestors are - and keeping them in remembrance - helps bolster your claims to particular farm land. Something along the lines of your great-great-great grandparents farmed this same plot of land (and here are their skulls in plaster) and so I have a right to that land.

Just like with the Hohokam example in Arizona, you see people in the early Neolithic Near East placing a lot of importance on building in place and the continuity of building in a place. For instance, placing very symbolic arrangement under the floors of homes, including burials. Nadel interprets these emplacements as possibly symbolic of first comer status (since they have no clear functional purpose in actually constructing the homes). They conclude that these arrangements

...may have been related to social behavior in which ownership and continuity of a specific location at the camp were represented on or under the floor.

In summary, ownership at least in some parts of the world is heavily tied to agriculture (since land ownership doesn't make a lot of sense outside that context). In some of these early agricultural contexts there is significant evidence for people placing huge importance on continuity of habitation in a place and the continued familial use of particular land (possibly through ancestor worship) that would have reinforced certain families as "first comers" to that community with rights to particular plots of land (likely the best farmland).

This isn't a comprehensive answer for how ownership develops everywhere in the world, but it at least gives you an idea of one possible route to private ownership.

Sources

Nadel, Dani. 2006. Residence Ownership and Continuity From the Early Epipalaeolithic into the Neolithic. In Domesticating Space: Construction, Community, and Cosmology in the Late Prehistoric Near East, edited by E.B. Banning and Michael Chazan. Studies in Near Eastern Production, Subsistence, and Environment 6. Berlin, ex oriente.

Vint, James M., and Fred L. Nials (editors). 2015. The Anthropogenic Landscape of Las Capas, an Early Agricultural Irrigation Community in Southern Arizona. (Archaeology Southwest Anthropological Papers No. 50). Contributions by: Dirk Baron, Owen K. Davis, David L. Dettman, Michael W. Diehl, Christopher Eastoe, Jeffrey A. Homburg, Gary Huckleberry, Richard I. MacPhail, Fred L. Nials, Manuel R. Palacios-Fest, James M. Vint, Chad L. Yost