I applied for our first set of notes in June (only 5 months after we submitted the application), because we were wondering whether they wanted the RCMP fingerprint report. It turned out to be a good move. I am not sure that if we did not order the notes and asked for the request that they would have eventually sent us the request on their own or not and if they were going to, there was no telling when they would have sent it.
In our case, I think it was a good time to request them. (Nothing had been started yet ... except our criminality check, which apparently was started in February and last we heard, was still not complete; I don't know why because my partner has a clear record and only really lived in Chile and Canada, which we have provided police reports that state this). Otherwise, I think waiting 2 or 3 months after your app has been opened is normally a good time to order notes, from what I have seen happening with processing with this VO.
We just ordered our 4th set of notes because we are in queue for an interview. We pretty much ordered notes every 2 months to see the progress on our app as nothing had been updated on our GCKey account since the beginning of March.