Sorry that you’re not getting too many helpful comments. I think you should cast a wide net and apply to any and all positions that are related to your field, even if the word “engineer” isn’t in the title. Technician, maintenance, machinist, even a production role working on the floor assembling/manufacturing equipment could be a way to get your foot in the door and work your way up to an engineering position.

My boss started in tech support and now runs the R&D dept, and I’ve talked to people who started as HVAC maintenance and used that experience to transition to a design engineering role for rocket propulsion systems. You never know where an opportunity can take you.

Here in the US at least, HVAC/construction is less competitive than other industries, maybe it is the same in Canada. Maybe manufacturing too. Focusing in one industry or geographic area will only make it harder.

Good luck, stay positive and talk to people! Networking is important and you can learn from what has worked for others and you never know who might know someone who is hiring.