I am pretty sure it has to go up the judiciary chain of command. I doubt highly that the Supreme Court would allow skipping over lower courts as acceptable.
Since the District judge ruled to set aside the lawsuit and injunction, the EO stands until the libtards appeal and get another injunction. In the interim, Justice can act on the EO. Ice has got a free hand.
No, the Constitution specifically states the Supreme Court has primary jurisdiction in matters of States vs Feds, Ambassadors and a few cases.