There can be some issues moving chicks to the coop. My grow-out coop is elevated, I think that causes me some problems. I usually don’t have these issues with my two coops at ground level. My grow-out coop is about two feet off the ground.
I normally keep the chicks in the coop by itself for about a week before I open the pop door to their run. Sometimes all the chicks are on the ground within 15 minutes of opening that pop door, sometimes it takes a couple of days before all of them venture out, I let them decide. Normally they all do get out that first day.
It’s very normal that they go to sleep on the ground under the pop door the first night, no matter how long they have been locked in the coop. After it’s dark enough to catch them easily I toss them in the coop and lock them in there. My broods are normally in the 15 to 25 range, not three like yours. On extremely rare occasions I only have to do this once. Sometimes it takes three weeks before all of them put themselves to bed. What normally happens is that a few start after a night or two doing this and all learn within a week, but each brood is different. And since you only have three my guess is that they will all want to be together, wherever that is.
In my opinion, the main benefit in keeping the nests blocked until they start to lay is that you have trained them to lay somewhere other than the nests so you get to open a new thread about how to get your pullets to lay in the nests. It helps keep the forum going.
My brooder-raised chicks normally start spending the nights on the roosts around 10 to 12 weeks of age. I have had some start about 5 weeks, I’ve had some go longer, but 10 to 12 weeks is a good average. When they start roosting at night will be important to you.
I don’t know what your coop looks like internally. With only three I’d assume it is pretty small. Typically chickens like to roost on the highest point available. If your roosts are the highest thing in the coop and there is ample room, they tend to roost on the roosts, not in your nests. But even then, sometimes one or more will sleep in you nests. They are not that consistent in behaviors, there are always exceptions to what they normally do. If they are going to sleep in your nests, I’d want to know it before I get poopy eggs so I can fix the problem. To find out the nests need to be open before they start to lay, not when or after.
Normally about a week before they start to lay, the pullets start looking for a safe place to make a nest. I want them to include the nests as part of that search. That can’t happen if the nests are blocked. Often part of that search includes some scratching. This can help you find another problem. If you find the bedding and maybe a fake egg on the coop floor, your lip is probably not high enough. You may need to modify your nests before good eggs wind up on the coop floor or an egg gets cracked when laid because you don’t have bedding in the nest or there is some other problem.
For these reasons I want the nests open about a week before they start to lay. I’ve had some pullets start to lay at 16 weeks though that is really rare. So my goal is to have the nests open by 15 to 16 weeks. There is nothing wrong with leaving the nests blocked until then, that may help train them to sleep on the roosts instead of in the nests. If yours are late to start roosting, at about 13 or 14 weeks you may want to start moving them to the roosts after it is dark to try to train them to sleep up there.
I never blocked my nests and it was never an issue, but with some people it is. I now have older hens so I cannot block my nests. When I integrate new chickens it sometimes becomes an issue, so I put a juvenile roost in, above my nests, lower than the main roosts, and horizontally separated from the main roosts so the chicks have a safe place to go that is not my nests. But you are not integrating, this should not be a problem for you. If your roosts are higher than the nests and they can get to them, you should not have problems. But if you do and you have a big enough coop so you can do something in there, we can help you fix that problem.
Good luck!
I'm going to turn on the automatic dawn/dusk function for my coop door and see how that works. 
