It is my grumpy observation that new (and old) beekeepers crush, main, injure and kill a lot of queens by over-inspecting the hive.
I cringe everytime I hear them say "I went through my nuc today and I found the queen". Why? If a new hive is fully drawn, add a super, but what good reason on this green earth is there for messing with the brood frames in a new hive. Let them alone, they don't need you invading their home more than absolutely necessary.
So where do we go from here:
1) sometimes brood comes in cohorts, after a hatch there is a lull, or a shift to nectar collection and away from pollen. Or just a break in the bloom as summer shifts into gear. How's the weather been?
2) if there is worker larvae you have a laying queen in the last 4-8 days, so why would it just expire?
Buy a mated queen -- and you will have new larvae in about 10 days. You will have spent big bucks for the freight and the monarch. The reaction to the queen cage could determine if the bees believe themselves still queen-right. If they try and mob the cage, they are likely wanting to kill her. If (after the intial chaos) they settle down to just a few attendants (check on day 3), it likely they want her to become their new monarch.
You might end up with 2 queens (as you discover you had a monarch all along). Come up with a contingency plan for starting a second hive using the duplicate, expensively obtained, but redundant queen -- Buy a frame of capped brood, attendant nurses, and a couple lbs of field bees from someone locally. Advertise on Craigs List, etc.
Others advocate getting frames of open eggs so a hive can raise an emergency queen. In my experience this has a low success rate with new or weak hives (it works with strong established colonies). You need 21 days until the mating flight, and another 22 days until you have ANY new hatch. Return from the mating flight seems pretty low, with high mortality. By the time a weak hive gets a second brood to begin hatching, the old bees are likely too few and too tired to get the hive off the ground. Method might work when you supplement weekly with fresh frames of capped brood (essentially adding about 5000 young bees per week. But even with a substantial bee yard that is a lot of disruption to the donor hives.
Short answer might realistically be: Catch a swarm, try again. You have all the equipment, and the drawn combs will help.