Does a store have to prove it inspected the premises before I can win a slip-and-fall claim in Ontario?

Not quite - the burden works somewhat differently. A store does not need to prove the premises were flawless at every single moment, but under the Occupiers' Liability Act it generally does need to show that it took reasonable care, which in practice usually means demonstrating it had a reasonable system of inspection and maintenance in place and actually followed it - things like regular walkthroughs, cleaning logs, staff trained to respond promptly to spills or hazards, and an appropriate response to weather conditions on the day in question.

You, as the person who fell, generally do not have to prove the store already knew about that specific hazard in advance; the real question is whether a reasonable occupier, taking reasonable care, would have identified and addressed the hazard before someone was hurt by it. Because of this, inspection and maintenance records - or the absence of them - tend to be central evidence in these claims, which is one reason a store with thorough, well-documented maintenance practices is in a considerably stronger legal position than one that cannot show it had any real system in place at all.