Ok but you can't apply unless you have a medical and since there's only 3 AeMCs that can issue an initial one and 2 of them already offer November for appointments, I picked the earliest date which was beginning of October.
So basically the CAA is not telling the truth when they say "Deadline is 31st of December 2022" because they argue "If we can't get it processed until 31st you won't get the licence".