You have to be in Ontario for 90 days to get OHIP regardless of the day of the month or anything else. You can get temporary insurance that will cover emergencies, and, if you pay more, some pre-existing conditions. We used this site to find plans and chose Destination Canada with $0 deductible and the maximum plan limit of $300,000 just to be safe:
https://arbetovinsurance.com/new-immigrants-canada-insurance/
So far we've found care to be cheap. One walk-in I went to was $100 but another is only $60 and both have good doctors. We haven't submitted claims for reimbursement yet (we have to drive to go use a printer for the forms) but as those are cheaper than we'd pay for an appointment in the US with insurance, we won't be too upset if they get denied for some reason. Medications have also been very cheap, and we're just using our US HSA account to pay for it all anyway.
Another consideration depending on your situation is COBRA if your insurance prior to leaving the US was through an employer. It's very expensive as an option but it's good to be ready to use it in case of something truly catastrophic that might push the payment limits of the temporary insurance plans. You have 60 days after leaving your employer or that insurance ending (not sure which since ours were the same day) to opt in so if you're in that situation, keep the forms your employer sends out handy so you can submit them and back payments on the monthly premiums if someone in your family has something terrible like a stroke or extremely bad accident happen.