The US Constitution does not allow a treaty to be enforced unless the Senate ratifies it. The rest of the world operates on the signature of the leader concept. Customary international law” does not trump the Constitutional requirement of Senate ratification.
The Paris climate accords is the latest example. Obama signed that treaty, but did not submit it for Senate ratification. When Trump came in, he pulled us out of it.
And the Supreme Court could not force anyone to obey a treaty without it being ratified.