No, the TRP would not have been a good option. It would have been a very very bad option. Applying for the TRP would really only be possible if your friend was out of status in Canada. TRPs take around 1.5 years to process these days so it means your friend would be out of status in Canada for a very long time and this would have almost certainly created very big issues for the PR application. So for many reasons, the TRP would not have worked. Applying for a TRP now isn't possible and doesn't make any sense. If you apply, IRCC will say you don't need one (plus you probably won't have a result for close to two years).
There are situations where a person can qualify for an LMIA-exempt closed work permit tied to their specific employer if their job is LMIA exempt. These situations are pretty limited. You'll need to research what's possible for you based on your occupation / employer.