Good luck, I think you’ll find the local gun club pretty painful. Generally it’s the classic social situation, you’ll awkwardly have to break into developed groups who will be keen to protect the information they’ve assembled and hard won on spots and so forth. It’ll be a slow road of making friends who will in turn be willing to help you out. Generally the hunting and spots will be very mediocre as well, if easy to break into the group.
The honest answer is if you have the intense urge to really do something, bust out of your comfort zone and just do it. Drive twelve hours if need be and learn up on YouTube, and give it a go. Ontario has a spring bear hunt again to my understanding and that could be an ideal start, with any small game on the side that may be open as possibilities. I’d get a second hand canoe, a good tent, fishing gear, and go live. That package works anywhere in this country.
Hunting by and large is best engaged in as a long game, a weekend makes it possible, but the real joys will come with week long trips and beyond. I’d personally aim for longer trips, less often, rather than trying to day trip. My hunting personally stagnated until I accepted that fact myself. I grew up on a large farm the family sold when I was a late teen, which completely turned hunting from a backyard activity on a whim to a sudden logistical challenge. Giving up on trying to hunt locally was a blessing to me, and brought the real adventures. And really, you’ll do better on your own if motivated, instead of spending years second fiddle in a group with marginal hunting areas.
I’d also be open in your case to a guided hunt in your own province, though cost is a factor there.