Private property requires that a private individual stake a claim to it. Private property is mutually exclusive of a state. The state [typically] is the primary violator of private property by enforcement of some shared mode.
This is not actually how it works in the real world. Private property cannot be upheld by individuals alone because of unsolvable issues in legitimizing any property claim, and therefore it is absolutely impossible to practically have any private property at all without having a state.
Indeed, looking back at history, the State was created essentially the same time that private property was created. This is not a coincidence.
Odd. I would only assume people kept possessions they made (tools, weapons, trinkets, etc.) prior to any formal states existing (or pooled them voluntarily). But, then, you get into _de facto_ states and what that potentially means.
Here it is useful to make a distinction between personal property and private property. The idea of having ownership over your direct fabrications is of course natural, but even then was fluid and affected by community need strongly.
Private property on the other hand, for example the ownership of land or resources, did not exist until the creation of the state, because private property in this sense was not possible without it.
In actuality, even some agricultural civilizations didn't develop private property, and it turns out that those that didn't are also the ones that didn't develop the state.
Indeed, looking back at history, the State was created essentially the same time that private property was created. This is not a coincidence.