First, If you want the bees to draw out comb, you have to feed them syrup continuously. If there is a flow available from forage they will slow down or even ignore the feed. Soon as the natural flow slows or is not of their taste for the day they will be back on the syrup. If there is no appreciable flow nor syrup, they will not make wax, they will not draw comb.
Second, to draw comb they have to have alot of bees of the right age. Not all bees can make wax all the time. There is a certain age that they are wax makers and that is only for a few days then they move on to other chores and the next wave of young bees become wax makers. You need to have bees and a steady rank of ages of bees passing through the wax maker age stage. If there is a gap in the ranks as the bees age that gap appears in the wax makers. At that time drawing of comb will stop, and combs may even contract a bit as the bees chew off balls of wax and take them to use elsewhere for example for capping brood cells.
Going to your question as to when to add a second box. Answer is add the second box as soon as they have enough bees to patrol it AND that the day and night time temperatures are warm enough that they will not lose brood from tightening the cluster every night. Overnight temperatures always above 15 deg C.
For your question as to how fast they will draw out comb and fill a box. Just as an example: When I need a bunch of new frames, I select a strong hive of 1 or 2 deep brood boxes (langstroth 10 frame) that is established and has the brood boxes already established and utilized. In warm weather and a good natural flow on ... Plop on and entire box of new bar 10 frames of foundation and put a hive top feeder half full of syrup on top of that. Under ideal conditions they will draw out every frame and half fill each of them in entire box in one week.
Sounds like you need to:
1) put continuous feed on your nuc/hive
2) make sure the queen and brood are healthy and expanding, giving a stream of ages of bees passing through wax maker stage
3) check your weather pattern, ambient temperatures, to know if conditions are favourable for the nest to be expanding without suffering a set back. Keep them tight if it is cool. If it is warm, add space and do so regularly to make them feel like their house is always just a bit too big.
PS: do not go spending unnecessary time shifting frames around. Bees spend a spectacular amount of time undoing and redoing work to correct what the beekeeper did to them. The beekeepers do not realize how badly they set back new colonies and nucs. Soon as you put the lid back on the bees get busy to undo what you did and get things back to where they want it. Nothing else goes on and after that will they move forward again. They will not draw comb on the frames you want nor the way you want. They will draw comb and arrange the way THEY want it. So just leave them alone if you want them to expand. Your only role is to control pests and diseases, give them space to live, give them support resources when they need it, and all otherwise let the bees be the bees. So, just keep the feeder full and let them have at it. Remove the odd piece of wild comb of course but otherwise just stay out. When they are full up into the second box and moving into the third, only then may you start thinking about frame manipulations. At that point you will have less impact on their overall master plan. They will also have a lot more bees available to undo the mess you ve made.
Does that help?
