Normally the queen will start laying a few hours after release, but not always if the hive was truly queenless and in this situation they would be hopelessly queenless their disposition would be loud and they would be flying into your veil acting very anxious . since they are mellow this indication would give me hope that for some reason she just is a slow starter. This sometimes happens because of dehydration during the shipping transit, and it takes a more time to build her back up. I have found a high percentage of package queens are superseded in the first month.
My suggestion would be 1) leave them alone for two more days then check for eggs again. If none found, look diligently for the queen if you can’t find her consider the hive queenless 2) If you have a second hive take a frame of open brood, and install it in the queenless hive. Make sure some of the brood is between one and three days old. They will be able to raise another queen.
If you don’t have a second hive, find a supplier and quickly order a replacement queen and re-introduce her, if they go queenless long enough workers will start to lay eggs which will be all drones then you have a whole new problem to deal with. This is why I always recommend someone that is starting into beekeeping to always start with two hives.