Absolutely wrong. First, government as you speak of it came many thousands of years after hunter-gatherers, but aside from that, why would there be any need to protect property? For most of human history there was simply no notion of "private" property but rather everything was held in common. You have it all backwards.
I can accept that correction and the one before it, thanks for clearing it up for me. No straw men there at all. My monkeyman with a stick though does represent the first primitive forms of government, the Patriarchal rule by the strongest monkeyman in the tribe. His property was counted mostly in females and the weaker males better leave em alone or they will get poked with that sharp stick. All that was really tongue in cheekish though. Did you ever see "The Gods Must Be Crazy"? the introduction of a new tool(a coke bottle) became an object of envy and trouble within a primitive tribe. As you say, there was no concept of "private property" until this unique item came among them.
Good coffee, good weed, and time on my hands...