IMHO, there is no single answer to this question. It largely depends on the way you are "chilling". It ranges from:
- Leave the pot on the counter until cooled to room temp, then stick it into the fridge until cold. Could be anywhere in the range of 2-6 hours, I guess.
with a bunch of variations up to:
- Transfer custard from hot pot into a flat, pre-chilled metal bowl or baking tray, plunge bottom into a salted ice bath (or pile of snow if it's freezing outside) and stir constantly with a rubber spatula. Should be cold within minutes.
So what would I do? I'd make the custard a day in advance, let it cool somewhat, then freeze the cubes over night. Never bother about the given 4 hours first freeze, because I assume this is a minimum time to get the cubes frozen fully. Finish the ice cream 4-5 hours before planned serving time the next day, because it might get too hard if frozen too long, but this depends on the recipe and I can't say for sure what the texture would be in this case.