Permanent Residence visa processing in Canada & domestic student treatment

[Joe VL]

Hi! I am in the process of getting a Permanent Residence visa in Canada. It should happen within the next several months. I know for sure that I'll want to get into a Masters (in order to do a Phd afterwards). I do  have already a (coursework) MEng in Mechanical Engineering from Texas A&M. I am eager to start applying before the PR visa process finishes, in order not to waste time (given that I would be actually applying for Fall 2020 and, by then, in all probability, I should already have my PR). Is that feasible? In other words: how long within the process of application for enrollment in a Master degree course as a domestic student in Canada is it necessary to hold the PR?