The university degree I'm willing to join is actually giving Cat C licence according to Part 66
I would check that out with the NAA of your choice, if I were you.
Even if you can get someone to issue you with a Cat C licence after 3 years experience (you would need that long or more to get the Cat B licence, by the way), with or without a Cat B under your belt, I would hope that in the real world any employer would suggest you go away to get many years real experience, then try again. MROs do not need very many Cat C holders to function well, and there's no shortage of experienced Cat C holders who are working normally as Cat B.
Employers are unlikely to risk their Part 145 approvals by employing a degree student - with 3 years experience as a fitter in a hangar and/or on the line - to sign off large passenger aircraft after base maintenance. Such a person is usually called a "Trainee".
If you get a Cat B you will have obtained 3 - 5 years experience to achieve that. Another 3 years working as a Cat B gives you 6 - 8 in all; you might get a Cat C after that, but probably not a job in that capacity until someone retires.