[a-priori]

Well yes, as soon as a creature needs to expend energy to obtain a thing they plan on using later, another creature is going to try to obtain it in a simpler way: by stealing it. And so, even apes and birds have a concept of 'property': things that are theirs, usually cached food, that they will take pains to hide and/or defend.

With humans it isn't quite so clear. The default societal structure for humans is the band, which is basically an extended family unit. In a band, property is shared by the group. If a member of another band sneaks in and takes something, that's theft and will result in retaliation. So a concept of property exists at the band level. But I don't believe that individual members of a band have stuff they are allowed to use but no one else.

It's only in more complex societies that private property at the individual level definitely exists. But these societies also have some form of government, even if it's just a tribal chief.

So if by 'property' you mean private (i.e, individual) property, it's not quite so clear which came first: property or government.

[iopq]

Except that's not true. Monkeys are supposed to give the eggs or other food items that they find to the senior members of their group. But sometimes they'll eat them when nobody is looking, or if they create a diversion (like they'll call like a predator is coming)

so theft can be done in group, especially when there's scarcity