The Constitution does not limit due process protections only to citizens or to those who are here "with permission." The Fifth and Fourteenth Amendments use the term "person", not "citizen," and the Supreme Court has consistently interpreted this to mean everyone within U.S. borders--including undocumented immigrants.
Whether someone is here legally or not is irrelevant to this point: due process is a constitutional guarantee that applies to all persons within the jurisdiction of the United States. This has been upheld in landmark rulings such as Zadvydas v. Davis and Yick Wo v. Hopkins, both of which affirm that constitutional protections extend to all within our borders.
Your argument about "shortcut-caliber basics" and "permission" is a mischaracterization--essentially a strawman. The law does allow for expedited procedures in immigration matters, but those procedures must still conform to basic due process requirements, including notice and the opportunity to be heard.
So no, due process is not contingent on prior permission to be here. It is contingent on presence within U.S. jurisdiction. That’s not an opinion--it’s settled constitutional law.