As I understand it the judge cited a very specific immigration law.
Unless the judge’s interpretation of the law is wrong and that opinion is overturned by an appellate court or SCOTUS, then it’s not within the President’s authority (as much as I would like it to be). The President is sworn to uphold the law. And this judge has ruled that the Congressional intent was clear that anyone no matter how they got here can apply for Asylum.
Maybe Trump can consider that they broke the law by entering the country illegally in the asylum process and reject them after consideration. But if the judge’s ruling stands, then Trump has to allow them to apply even if he rejects their application after consideration.
They have to get in first !!!
The judge cited an unratified UN guidance document, as I understand it. Your position is not without merit, but at the very least a precedent that only SCOTUS can rule on this subject.