This is silly. First of all, only wealth can be created or destroyed, not poverty, which is the absence of wealth. My ape ancestor swinging from a tree without easy access to food, clothing, shelter or medicine is poorer than I am, full stop.
Second of all, there has never been a paradise where resources are communally owned without clear limitations on the use and distribution of those resources, usually at the behest of corrupt, tyrannical or murderous leaders.
Third of all, the existence of a monetary cost or private property is moot when it comes to defining ownership. An eagle doesn't use money or property laws to own his nest, but it's not like any other eagle can use it without cost.