Well...for restricted stuff - handguns - You sure hit it at the wrong time. I believe in Ontario, you must be a member of a club before the CFO will approve a transfer. I could be wrong on that. I haven't looked into that lately. If that is the case, getting a handgun into your name before "the freeze" takes effect is going to be pretty hard. On top of your time constraints, you've got the near zero inventory issue as well. Dealers are selling out of everything fast and hard. Hopefully one of the guys from Ontario can offer you better direction than I can on the whole issue.
Non-restricted stuff isn't an issue. That's still business as usual. There's places around the GTA to buy long guns. Just do a google. Al Simmons in Hamilton, Bass Pro/Cabelas north of the city. Possibly some Canadian Tires are dealers just outside the GTA. I'm sure you'll get lots of responses. Check out our Marketplace for private sales, Gun Post, Town Post etc are also places to look. Kijiji and Facebook Marketplace don't allow gun sales so don't bother with them. If you're buying off any of the gun sites, including ours, be extremely careful making deals with people who have just signed up and have 0 for a trader rating. There have been plenty of scammers over the years and once you send them that EMT, it's pretty much impossible to get it back.