They don't need an hour of out of cage time a day as much as they need a at least an hour of interaction a day, most can be done in the cage. Things like sitting by the cage and talking, reading aloud, singing (if you can sing) or playing and instrument (if you play), playing with him in the cage like petting him, hold chews for him to chew on, letting him climb on you, and hold him. You can also hand him something every time you come near the cage, could be a treat, a toy, a chew stick, or a bit of hay or pellets, that way he associates you coming to the cage with getting something good. How long the bonding process will take is hard to say, could take weeks or months, but for the most part it takes most chins at least a week to settle in to a new home and start to trust, up to a month is not uncommon though. That means a week to a month before they even start to trust not a week to a month before they trust you. Full trust takes years in most cases, but I would say expect up to a month before you can try playtime again.
Once you get a bond forming it's best to do playtime in a chin proofed area, like a room without anything he can get under or a playpen. There should be nothing he shouldn't chew accessible as well as nowhere he can go that you can't get him. You can block off areas using cardboard boxes or critter fencing, or use it to make a playpen area or block off an area for play. You can also use fencing around the cage and so the chin can come and go from the cage on his own, when it's time for playtime to end if he hasn't gone back himself you can make the pen smaller so it's easier to catch him or he goes back in the cage. Another trick is to use the dust bath to catch him, most chins will run to the bath and then you can scoop him up in it, most chins catch on quickly to that trick though.
Keep in mind that chins do hold grudges, so if you end up chasing him that is only hurting the bond, and could be proving to him you are not to be trusted.