As
@whisperingrock said, this can be quite late. I have known people to join a course a week or so after it started (although I wouldn’t advise that).
Particularly with the SQE, I suspect these courses will be less and less popular over the coming years and so you won’t struggle to get on them if you have a 2.1 and can find a way to finance the course.
Obviously you mentioned getting sponsored by a firm, but that could determine everything for you anyway. For most firms recruiting for 2023 this year (who will sponsor you) they probably wouldn’t rush you on to this year’s course anyway.