As you rightly say, it will depend on a lot of things. I personally began to see nectar in the cells about 2 weeks after putting the Flow super on top of the hive. They started to put nectar in the middle frames first, so looking through the side observation window, I couldn't see it. I had to do a hive inspection and lift the Flow frames.
If you have a very strong hive, or a very intense nectar flow, they may even fill the super within 2 weeks. However, I think that is more likely if the super has been used before. Somehow they seem consistently to fill the frames much faster after the first time.
Some people found that the first year, the bees investigated and waxed the Flow frames, but didn't actually store any nectar in them. However, the second year, they really took off.
Long answer to an apparently simple question.