I started leaving it open for him a day or two after he came home. However do consider that you need to have a lot of free time with him during this time. You can't expect to allow him out for a few hours as you haven't built trust with him yet. So scooping him up and setting him back in the cage isn't really a possibility. You need to wait for him to go back for more food or water etc. When my guy came home he was very shy for a few weeks. I left the door open, but he didn't decide to come out for a few days. Then he start spending time on the top of the cage for breakfast. It took him a few months before he felt confident navigating the house.
Hopefully this helps