I agree with the others, that coop is no good for any number of chickens. It's what manufacturers sell to make money because it looks cute, it's conveniently small, and cheap-priced, so it's easier to sell than a real coop. It's a common trap newbies fall into, and come to regret later. Start looking for a real coop now, at least 4 square feet per bird, but give yourself leeway in case you want to add more chickens later. Very few people start with 3 and stay with 3, without adding any more... Chickens are cute!

When you get the real coop, no matter what age the chicks are at the time, lock them in it and keep them in it for about a week. Don't let them out into the run. That's the general strategy for transitioning chicks out to a coop (if you don't already have a flock), but is impractical in your current setup because the coop is so tiny. It will "home" them to the coop. They'll get familiar and attached to the space, and it will feel like home, like shelter, like protection to them. So when they go outside, they'll want to come back inside for protection and to sleep (though they'll still need help figuring out when/how to go inside for bed). This homing stage is important, and very effective. It's funny to observe how it works for other structures, too. For example, I brood chicks in the house often, and when I take them out for field trips to the yard, I bring them out in a small dog carrier. At first they are terrified of being in it. But over time, they get used to the carrier so much that it becomes their safe place when being somewhere even scarier, like the back yard. So while they are happy to explore the grass and run around, when a truck thunders by or a dog barks, they all shoot themselves back into the carrier! So that's how you want your chicks to feel about the coop - that it's their safe space, their shelter, to head into when scared, when it's raining, when it's getting late and time for bed. If you introduce both the coop and the run at the same time, neither will be more familiar or comforting to them, so they won't prefer the coop for protection or sleep. Chickens don't have an instinct to go into an enclosed space for protection, like burrowing animals would. They have an instinct to go high, up in the trees, both to sleep and for protection. So if they don't have the familiarity and habit of the coop, they'll want to stay outside to sleep, perched on the highest thing they can reach - or huddled in a corner on the ground until they learn to go high and roost.