For the CCF this will be rather variable. Your own Contingent might have a view (I don’t promote to Sgt without an MOIT course, but we run an in-house tri-service one using the Army CFIT manual). There’s not usually a requirement to have done one of the Part 3/Advanced subjects.
Don’t confuse this with either Instructor Cadet (MOIT compulsory, must have passed Part 3, must be 16) or Flight Sergeant, where the TEST Sgt will have to approve the promotion and where you must have passed Part 3.
Have you spoken to your Contingent or Section Commander? Depending on how integrated your CCF is you might find the former has to approve the promotion; if the RAF section is pretty independent then it might just be up to the latter.