NO --- do not keep them in a dark barn for 2 weeks. That is very bad. DO NOT FEED YOUR GOSLINGS SCRATCH! Read the lablel on these things you're feeding the geese.
It's one thing to feed them crap if they have access to free pasture and grass to offset the garbage you feed them but if you pen them up in a pen lock them away from their natural habitat which is grazing and they need that grass for development and survival and feed them garbage it is like locking your kid up and feeding them nothing but pizza and not letting them move for the next 6 months.... they would be a fat, lazy blob with no muscles and unhealthy unable to walk/etc!
You can't turn them out and let them just run free it would be like turning out your other animals without fencing/pen/etc. It is dangerous and they would definitely be killed - the little ones first probably. Owls, coyotes, cats, bobcats, dogs, coons- - all attack geese and will get them for sure - they do not fly up into trees and are voulnerable on the ground. If anything get yourself a 100' roll of chicken wire and make a makeshift fence coming out the side of the barn there - it looks in the pictures like you have plenty of green open air and grass.... just jam some poles into the ground and run the wire around it and keep an eye on them constantly as long as you don't have stray dogs or dogs running around then they should be fine in there - just keep an eye on them.
They need to graze for a while - not just 10 minutes. You'd be surprised how just a light throw up little fencing keeps them in... You've got the grassy area there - just put some water and a food pan in there (make sure you pick up the overspill so it doesn't mold and babies pick it up later and die).
If you're going to have geese, you need to put them in their barn stall at night with some water in there for the babies to have access to. Let them out in the morning give them their feed and usher them into a pen or tractor to move them around on the grass or let them graze during the day - make sure they ahve shade.
You can not just keep them in the barn for 2 weeks or whatever and throw lettuce in there. Lettuce is ZERO nutritional value and is not grass! These goslings are growing. They grow and change every day. The upcoming next 4 - 6 weeks for them is critical as they will be putting on feathers and need to stretch, flap and run.
When they are all full grown (and fully grown) you can turn them out during the day if you don't have dogs running around and let them graze and wander.... they will likely hang around the pond.
You can herd them you know... down to the pond, watch for them, stand there and let them enjoy and then herd them back up to the barn/house/pen when they are done on the pond...... Geese don't run crazy like chickens! They are slow walkers and easy to herd.