It varies a bit between individuals. When my bun Vilde came to me, he had a cage with him from his old home. I put it in my bedroom, left the cage door open but blocked access to the rest of the apartment with a grid. He stayed in his cage for about 2 days, then he started to explore. He settled in very quickly, but he was 6 years old and has an outgoing personality. Other buns may need quite a bit more time.
The most important thing is to provide a hidey house or/and a tunnel, so the rabbit knows it has a safe place to retract to should need arise. A hideyhose can be made from a cardboard box. It should have 2 door holes, because that’s how rabbits make their warrens – they always make sure there’s an “emergency exit”.
If a bun has a safe hidey house, it feels safer and dares explore more and sooner.
Another advantage with starting with a smaller area for the bun is to allow the bun to choose a toilet-spot which is conveniently located for both the bun and the human. The cage/pen is a good place to have food and water and toilet in.