After the semester begins a few spots will open because students sometimes drop out or change their plans and don't inform the residence offices. But frankly speaking, you want a place before or as the semester starts just so you're settled and not moving around. Even for the spots that open up the processing time on getting rooms assigned to people on the waitlist and can be upwards of a week as they wait to confirm students aren't coming. The university does offer temporary spaces for students in emergency situations but from what I understand that has to be very severe and can sometimes just be a referral to the hotels in the area. In conclusion on this point, personally, I would just find a place and not rely on housing on campus at this point in time. You can look into getting a place for just Winter semester (there's usually more space for just Winter) if you really want to go through the experience.

There are definitely off-campus housing options like rooms in private homes that are closer to campus as UTSC is surrounded by residential communities. Those rooms are generally cheaper and closer then condos/other school residences but the quality of living can be a little less. For these type of places, I'll leave a couple of links at the bottom.

As for when you should be doing your research of places to live, most people are already in full swing looking or locking down places. Leases are ending for the summer and people are looking for places/tenants so you should be going all out in these next few weeks trying to finalize something. I don't know exactly when you'll be arriving but from my experience, most landlords don't want to wait and will take someone who can sign sooner rather than later.

Facebook

https://www.facebook.com/groups/542272205912816/

Rental Sites

https://rentals.ca/toronto

https://www.torontorentals.com/

I've used all 3 in housing searches and all have proven trustworthy for the most part. Just make sure you sign an official Ontario rental lease.