For the Province of New Brunswick, the rules are stipulated by the APEGNB (
and it looks like it is possible to become a PEng without an engineering degree.
I have actually been part of the evaluation board that examines foreign-trained engineers for admission, but those are people with engineering degrees from other countries, which is obviously different from your case.
To quote:
The steps required are as follows:
Completion of an undergraduate degree in engineering/geoscience from an accredited university program or other academic or technical institution recognized by the Council. For candidates who have not completed an engineering / geoscience undergraduate degree from an accredited institution, a series of examinations may be taken as determined by the Association.
Application for registration as an Engineer- / Geoscientist-in-Training with the Association.
Approval of the application for EIT/GIT registration by the Admissions Committee of the Association, and subsequent ratification by the Council of the Association.
Completion of the required amount of certified engineering or geoscientist experience, under the supervision of a Professional Engineer / Geoscientist.
Submission of an application for membership to the Association.
Approval of the application for membership by the Admissions Committee of the Association, and subsequent ratification by the Council of the Association.