My thoughts are to get the nests in now. Don't go making changes to the coop when they are ready to lay. They typically don't like change so why take a chance in upsetting them at a critical time. Whether the nests are open now is a different question.
I don't know what your coop looks like, how big it is or how it is laid out. Where are you going to put the nests? How high especially. How high are your roosts and how much roost space do you have? These are critical factors.
I want the nest open before they start to lay for a few reasons. I don't want to have to teach them to lay in the nests if they have learned to lay somewhere else. That can be a harder habit to break than if they sleep in a nest.
If your roosts are higher than the nests and you have sufficient roost space it is unusual for chickens to sleep in the nests, especially once they are laying age. If they are sleeping in the nests there is a reason that needs to be fixed. That's another reason I want the nests open before they start to lay, so I can fix problems before I get poopy eggs.
My brooder-raised chicks typically start to roost somewhere round 10 to 12 weeks of age. I've had some start as early as 5 weeks, some take longer, but yours sound normal. The way the coop/roosts are set up may have something to do with that too.
Often, not always but often, pullets start looking for a safe place to lay a few days to a week before they start laying. Sometimes that investigation involves scratching to shape a nest. If you have your nests open and find the bedding and fake eggs on the coop floor that could mean your nest lip is too low. You need to raise it before freshly laid eggs wind up on the coop floor.
Some pullets seem to not have control over the egg laying process. They may drop an egg wherever they happen to be. But once they gain control of that process, where they choose to lay their first egg becomes their nest. I want that to be in one of my nests. As complicated as the egg laying process is, not just forming the egg but the behaviors that go along with it the surprise is that so many get it right to start with.
If your chickens are sleeping in your nests, there is a reason. One typical one is that the roosts are not higher than the nests. That's a design failure.
Sometimes you have a roost bully. This is usually when you have different aged chickens, not all the same age like yours. Still, it happens. One chicken is such a brute on the roosts that the weaker chickens look for a safer place to sleep. That can easily be your nests. I regularly integrate younger chickens with my mature flock and used to have that problem a lot. I fixed it by putting in a separate roost, higher than the nests, lower than the main roosts, and horizontally separated so the roost bullies would leave the chickens alone.
There is nothing wrong with leaving the nests closed until the chicks are roosting. If the roosts are higher than the nests and the chickens are in the habit of sleeping up there it is unlikely they will switch to the nests unless one becomes a roost bully. So when they are sleeping on the roosts is a great time to open the nests. I've had pullets lay their first egg at 16 weeks. That's really young but it can happen. I certainly want the nests open by then.
My nests are never closed. I have a mixed age flock with hens always laying so I want the nests open all the time. Integrating younger chickens with a mature flock I am at a much greater risk of having them sleep in the nests than you, but since i put up that juvenile roost it has not been a problem.
