Forget the natural part, the important part is coercion. You can't have socialism without coercion and initiation of force, you can have a free market though.
As I already said, most people probably don't share your definition of initiating force and coercion. You provide no reason why those terms should be based only on private property. If you define initiation of force as "initiation of force, except when i'm protecting property", then you can obviously come to the conclusion that you don't initiate force, but you are still initiating force by other peoples definition, unless you can justify to them the assumption in your definition.
You only have a free market without coercion as long as all participants act in good faith. Otherwise you either have to let bad actors get away with whatever they like, in which case you no longer have a market, or else someone has to coerce them into fulfilling their obligations.
> You only have a free market without coercion as long as all participants act in good faith.
No, you have a free market without coercion as long as there is no coercion. If some are acting in bad faith or badly, that's more power to the competition.
