Are your girls roosting yet? Will the roosts be higher than the nests?
I would put the nests in now and leave them open. Put the bedding and a fake egg in the nests now. I would not block them off. If you are going to have a problem I'd want to know now so I could fix it before they start to lay or before I taught them to lay somewhere other than in the nests.
Often pullets look for a safe place to lay before they lay their first egg. I want them to at least consider the nests. That inspection often involves scratching. If you find the bedding and fake egg on the coop floor they are telling you that you need to fix your nest. It generally means your lip isn't high enough to keep the bedding, fake eggs, and real eggs in. It's often a simple fix but I'd rather find out before I find broken eggs on the coop floor.
One concern is that your pullets may sleep in the nests. If your roosts are higher than the nests and you have sufficient roosts it's not likely but it can still happen. If some do sleep in the nests there is a reason. If you can find out what that reason is before they start to lay you can fix it before you get poopy eggs.
Good luck! Hopefully it won't be much longer before you see that first egg.