Does each individual on the planet have a natural or God-given right to live in the U.S.?
Yes , of course they do.
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They do what?
This is an either/or question, isn't it?
Is their right natural or God-given? Which?
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I'd say neither. And that doesn't matter, because neither Nature nor God is in charge of the legal aspect.
Those who are born here have a legal right to live here, as do those who have been legally admitted.
I don't think God or Nature get involved with this: when someone approaches the border, the one sure thing that does not happen is God booming in his best James Earl Jones voice "Come In!" or "Stay out!". Neither are earthquakes, tidal waves or volcanic forces likely to endorse or reject the admission or prevention of entry to any prospective immigrant. This means that God and Nature are silent on this issue.