I received a letter telling me that my request has been transferred to the responsible service. They didn't give me any file or application number. I received a job offer and I wanted to update my file, so I called them again so see how I can do that, but the agent on the phone there is no way to get the CSQ after becoming a PR, however, they can give me an attestation that I can use instead of the CSQ.
That being said, as a PR, you are legally entitled to live anywhere in Canada, and you don't even need a CSQ to benefit from certain services if you can prove you've been living in Quebec for more than 3 months. Some universities require 12 months for you to be able to pay a Quebec fee which is lower than the Canadian fee. So you can check each university if education is your goal.