What about a Full-Time Degree without the JAMB?
If you still want to avoid writing the UTME, some universities offer 12-month programs that only require you to obtain a Direct Entry form after completion.

With such advanced programs, you will be offered 200-level admission to the university where you completed them, as well as any other university that accepts them. The university programs listed below will allow you to gain admission without taking the JAMB.

Interim Joint Matriculation Board (IJMB)
Joint Universities Preliminary Examinations Board (JUPEB)
University Advanced Basic Science (UABS) e.g FUTA UABS
National Business & Technical Examination Board (NABTEB Advanced)
Cambridge Advanced level e.g UI Cambridge programme

After completion of any of the above programmes, you will obtain the Direct entry form which doesn’t require writing UTME. It’s through the DE form that you will choose any interested university you wish. If you meet a certain point required, you will eventually be offered admission