You’re more patient than me, I installed a 5 frame nuc 2 weeks ago, no new comb built although I can see a slight increase in numbers. Didn’t spot the queen when I inspected Saturday although I did have capped brood and larva so know she is in there and laying. Being impatient I pulled the 3 empty frames with wooden starters that come with the flow hive and replaced them with wax foundation frames I made up. I was feeding but it was attracting ants so have stopped as we have a good flow. I did get to see a bee emerging from a cell when I inspected Saturday so hoping the increase in numbers, along with a good flow might mean the wax foundation frames are the encouragement they need to start building.
For comparison I picked up 2 more hives a week ago (7 drawn frames) in 6 days one of these had built a full frame of comb, filled nearly 50% of the space above the frames with burr comb and had filled around 50% of the new comb with honey.
Any advice I give comes with a whole 2 weeks experience.
Do you have a good flow on? if not feed.
Do what you can to eliminate the SHB, if the bees are spending time defending what they have from beetles it is less time for them to build and I am guessing they would be reluctant to build more comb if they are struggling to defend what they already have.
Can you pick up a frame or two of brood from anywhere? It would increase number quickly, giving you more bees to work, more room for you queen to lay and should see things start moving a bit faster.
How often are you inspecting? I know being new and keen I have to resist the temptation to open the hive and am limiting myself to once a week to check their progress. I’m not sure how long it takes them to settle back into their normal routine after a inspection but every time the hive is opened has to set them back slightly and with a small new hive this may have a big impact.