So you are looking at 31 birds, and while the chicks are little, you can cheat a bit on your numbers. Some people have the misconception that if birds are raised together, they will always get along. They won't. They need space or you get very ugly behavior. For 31 birds you need a coop of about 12 x 10 feet. Even if they free range all day. The long nights of winter, most birds are roosted up about 14-16 hours a day.
4 roosters is bound to also cause very ugly behavior. Personally, I believe the least number of roosters is best for the peace of your flock. There will be a lot of tension in your flock as the cockerels come into their oats, so to speak. Again, space will help, but I would still expect a lot of tension, which tends to lower egg production. They very seldom will all just be nice.
Both statements above don't have anything to do with your question, but I think are valid problems. Chicken math has to work both ways - adding and subtracting.
As to your question, I like to get them in there early. 3-4 weeks. I create a shelter with a wooly hen, and a small pen in the run. If you use chicken wire, just section out a corner. I close up the shelter, and put it with the chicks in the coop at night.
After a week, of see no touch, I lift the fence about 4-6 inches off the ground. This allows the chicks to explore the bigger run on their terms. They can escape to the safety zone whenever the big world of big hens gets too much. The first day, I lock the hens OUTSIDE the run, and sit there with my coffee. Eventually the chicks will get brave and wander out. After a couple of them wander out, I chase them back in. They quickly realize that the safety zone is where to go when chased.
Then I let the big girls back in, and in a week, the littles are eating right next to the bigs, and it is over.
Mrs K