Not a silly question, i asked the very same thing the other day, to which i was told a couple of weeks, possibly longer if its a strong colony. (nice clear sunny days help the process)
Best to leave them alone from time of emerging while she embarks on her mating flights, i worked out roughly when my queen was due to emerge, i then gave them a fortnight before going back in, next inspection the frames were full of eggs, lovely sight and well worth the wait.
All of mine came from the same hive & were split at the same time. Nucs made up 21 May , all queens had hatched by the 9 June , 21 June eggs spotted ( no more than 3 days old ) in 2 , 30 June for the last one before any eggs were seen
I'm in a similar state. Dodgy colony, added test frame, went on holiday which helped control my curiosity, found sealed QCs had developed so have left the alone. I estimated the Virgin Q would emerged around 28/29th June and now I'm just waiting, waiting, waiting......I soooo wanna have a look-see! but not before the coming weekend.
Patience is definitely a beekeeping skill I'm finding hard to develop.
I had similar situation to Dewin Dwl, but perhaps 2 weeks ahead. Patience is the key. I inspected last week after leaving it alone for over 3 weeks. Found lots of brood, capped and uncapped as well as eggs. Did not see the queen.
It might be worth mentioning that there was lots of stores and pollen in the BB, and little activity in the super. Will they start moving the honey to the super to give the queen more spare? I hope they do, otherwise the queen will run out of space quickly.