It depends on what purpose you are ordering GCMS notes. But in general, if it's a TRV application, as soon as you have passed the normal processing time, or if you have received no update on your case since you applied, and if it's a Permanent residency application, it can be done at the second or third month since you applied. The same for the citizenship applications.
You can also order GCMS notes after your application for a temporary residence visa or permanent residence has been processed and a decision has been reached by IRCC (positive or negative). If the decision was negative, the GCMS notes will let you in on the reasoning of the immigration case officers behind the refusal.