1. The State Department can go as slow as it wants in vetting refugees and issuing visas.
2. The Constitution allows Congress to set the jurisdiction of the lower courts. President Trump should propose a law depriving all district and appellate courts any jurisdiction to rule on matters of immigration law (except for criminal cases like illegal retlentry, etc). Congress could decide to provide jurisdiction to one particular district court or to none at all, in which case challenges to his actions would have to be brought in the Supreme Court. Or Congress could establish a new special district court to deal with challenges to immigration laws and the President could then appoint new judges for that court.