You don’t need to call IRCC or contact anyone for your application number. First, they will send you a temporary application number (starting with "XG", like XG1234567890). After a few days, they will send you your permanent application number, which is the same as the XG number but without the "X"—for example, G1234567890.
You can only link your PR application to your GCKey account once you receive the permanent application number (the one starting with "G").
Until you link your application to GCKey, you won’t be able to check your status online.
If you applied for PR through a lawyer, the lawyer will receive the application number by email. You need to ask them for the number and let them know that you plan to link the application to your own GCKey account.