Patience is often a great tool and often in short supply. It could come in handy here.
I personally don't worry that much about what the nests look like. Dad used open nests (no top). I've used both open nests and nests with a top. In my opinion its another one of those things people worry about more than the chickens do but some people have strong opinions about it. That's all my opinion is, opinion. Still a look at the nests might be helpful. Pictures are often good.
Some pullets have control of the egg laying process from the get go. They search out a good place to lay before they need it and start laying right there. Others seem to have no initial control of the process. They might drop the first egg or several eggs wherever they happen to be any time of the day or night. Maybe from the roosts or just walking around in run or coop. Sounds like you have one like that. But eventually (often pretty quickly but hopefully within two weeks) they figure it out. Egg laying is a pretty complicated process from when to release the yolk to start the process, getting the components right, and then actually laying the egg. It sometimes takes a bit for them to work all the bugs out of their egg making factory and system.
Is your pullet returning to the same spot each day to lay her egg? If so she has probably determined that is her nest. Normally they scratch out a depression when they do decide it is a nest. Where is it, out in the middle or sort of hidden along a wall or in a corner. Sometimes just a shadow is enough to make them think it is hidden.
Is where she is laying an acceptable location? Would putting a nest in that location be OK with you?
I am a strong believer in the power of fake eggs, but Aart once had a pullet that would not lay in a nest until the fake egg was removed. There is just no telling how an individual bird's brain will work. That's one reason we need to be flexible.
If you run out of patience with her or don't want her to show the others it's OK to lay there, I've had really good success in retraining them. When I have one consistently laying in a nest I don't want her to, I lock her in a real nest when I catch her on the nest she prefers. She stays in there until she lays her egg, usually about 30 minutes but I had a hen that took three hours. Usually once is enough but that three hour hen had to go in twice on consecutive days to get the message. That was one hard-headed Speckled Sussex. She was also a nest hog. Not only did she consistently take three hours to lay an egg she would not share that nest with another hen. Most of mine do share.
Since your nests are open-topped you'd need to build one you can lock her in if you try this. I made two of mine with a lock, that has come in handy for different things.
Good luck! This kind of stuff can be frustrating.