I believe my hive is queenless, how late is too late to introduce a new queen?

I installed my first package of bees on 24 April. Since then I have inspected the hive 5 times and have been unable to locate the queen. Additionally I am seeing no worker cells and I believe the hive is 80%+ drones.

I see some eggs but there are often more than one per cell, which I believe is a sign that the workers are laying.

I have found what I believe to be empty queen cells.

I assume the queen had to at least initially have been successful since it’s been 8 weeks and there are still some workers?

Assuming I’m right and my hive is queenless, can I buy a new queen and install her? Or is it too late. Or, assuming I was correct about the queen cells, just hope they’re able to successfully mate?