My brooder is in the coop so a different situation than yours. Sometimes at 5 weeks I just open that brooder door and walk away. You can’t do that. For your own reasons you’ve elected to do it differently, I respect that, just pointing out differences.
I also have what I call my grow-out coop. For my own reasons I sometimes don’t just open that brooder door but move them to this grow-out coop, usually when they are 5 weeks old. It’s 4’ x 8’ and elevated with a section of run. It’s at the far end of my main run and the run butts against my 12’ x 32’ main run and also an area enclosed by electric netting, about 45’ x 90’. So I have lots of room for a flock my size and the chicks and adults can see each other when the chicks are in the run.
I normally lock them in the grow-out coop section itself for about a week to get them used to the idea that the coop is home and where they should sleep, but it never works. I think that’s because it is elevated. I have other set-ups on the ground and I don’t have this problem. The chicks consistently sleep on the ground under the pop door when I let them out to the run section.
My brooder-raised chicks tend to start roosting at age 10 to 12 weeks when there are no adults on the roosts. I’ve had some start earlier, some later, but 10 to 12 weeks is fairly normal. Until they start roosting they huddle together in a low spot. Since my coop is elevated the low spot is on the ground, not the coop floor. After they are let into the run section of the grow-out area, I go down after dark and toss them into the coop section and lock them in. It’s dark enough down there that they are easy to catch after dark. On bright moonlit nights that can be a bit more challenging. Some chickens get the message immediately, sleep in the coop. I’ve had some take three weeks to get that message. Most of the time it takes about a week to get all of them going in on their own.
After I am sure they are all consistently returning to inside the Grow-out coop to sleep, I open the doors to the main run and the netting area. That usually works out to about 8 weeks age. The young chicks soon go out in the other areas, but normally form a sub-flock and avoid the older chickens. They return to the grow-out coop to sleep at night.
For different reasons I sometimes leave the chicks sleeping in the grow-out coop section. Sometimes I move all or some into the main coop. When I move them into the main coop, often around 12 weeks old but can be later, I put the ones I want to move, usually pullets, in the main coop after dark and leave the ones behind locked in the grow-out coop/run area for a week. Sometimes the chickens being moved immediately get the message and start going into the main coop at night, sometimes it takes another night or two of putting them in. When I do this I’m down there pretty early the next morning to let them out of the main coop in case there are problems. There never have been but I still go down there early a couple of mornings to be sure.
A lot of people do it differently as you can see by Aart’s post. Nothing wrong with that, many things can work. I do think a key is how much room they have. If room is tight it could be beneficial to keep them separated longer. I’ve seen broody hens wean their chicks at three weeks so in some circumstances you can do it earlier than I do it. There are no hard and fast rules with this, we are all unique.
I find having separate permanent facilities can be extremely convenient in managing your chickens, it gives you a lot of flexibility. I have three different areas other than the main coop I can use to isolate chickens. There have been times all three have been in use.
How much room would I have in a grow-out coop for 20 chicks? First, I don’t believe in standard square feet per chicken numbers. You can follow the link in my signature for my reasons. How old will they be before you move them out? Will they be laying? Will you have a section of run dedicated to this coop, I highly recommend it. When will they have access to that run, what age and how early in the day?
I’ve housed 20 chicks in my 4x8 before, but that’s a big reason I often move some out by 12 weeks, even with plenty of access to outside, it gets really crowded in there. I don’t leave them locked in that coop section only after 6 weeks, they always have access to the run. My coop section is only for roosting, feeding, and watering. No nests. My floor is ½” hardware cloth so poop drops on through until they are older. At a certain age the poop gets big enough it doesn’t all fall on through, though a lot still does. I don’t know why the difference but for some broods that can be 12 weeks, for some 15. The tighter they are packed the more poop you are going to have to deal with.
For what you are talking about I’d be tempted to go with a 6x8 walk-in on the ground, or maybe even a bit larger. That will give you more flexibility than I have, though you may have to manage the poop more. If you are buying new materials, they normally come in 4’ and 8’ dimensions so these are usually good dimensions to use. 6’ isn’t all that bad because you can rip a 2’ section and add that to a 4’ to get there, plus with a 6’ width, the standard 8’ dimension gives you some overhang so you can put ventilation under that and still keep rain and snow out.