If people do not have any natural rights, this means they don't have a just claim or title.
Your belief that it is moral for them to have this claim, doesn't automatically make natural rights come into existence into the minds of others -- only in your own mind.
If you want people to have a just claim or title, then you believe in this concept and persuade others to believe in it. If enough people believe in it, then they will act on their belief and support it.
Obviously, human nature must be hardwired to believe is some version of property rights, just not enough as libertarians believe in.
I think that a better way to explain liberty is through the non-aggression principle.
And don't forget, anytime you talk about rights, some people think you're mean positive rights. You have to distinguish and explain the difference between positive and negative rights.