Why bake, cool then torch the creme brûlée; why not skip the cooling? Is cooling for setting?
Cooling for 4-24 hours is in almost every recipe I find.
Crème brûlée is supposed to be served cold, with a hard, crisp caramel layer on top. So that requires cooling after baking. The baking is needed to set the crème, it might just be a bit firmer after cooling. To ge the hard caramel, you need to add the sugar on top and then torch for a short time, just before serving.
You can't have the caramel formed during baking, or refrigirate after torching, as the caramel would absorb water from the crème and turn liquid (or at least get very sticky).