This is a tough issue and one I have no training on and little experience. The best answers come from people that have numerous, successful experience with the problem. I know how to keep puppies from crying the first night in the new home. Some dogs just seem to do it although their owners are doing about the same as those that don't have the problem. Do a search on it here, you will find lots of questions, but few reports that something worked. Much of what you read is emphatic about dogs not fouling where they sleep. Dogs sometimes don't seem to have read those books. Why they are doing it? Resentment at being crated, stress, poor previous conditions? The puppies I get have extraordinary care. I have visited at least one home where the birthing box is in the living room.
There are ways of coping with it. A rack or a grid is highly effective at keeping a puppy out off urine, or in this case, a vegetable bin with holes in it.
I have suggested trying wood chips in the crate, but nobody ever posted back that they tried it, and if it worked.
Stronger leadership should help if stress or resentment is the problem. Dogs see all the people and dogs in the household as a pack with each having their own rank in the pack and a top dog. Life is much easier if the 2 legged pack members outrank the 4 legged ones. You can learn to play the role of top dog by reading some books or going to a good obedience class. A good obedience class or book is about you being top dog, not about rewarding standard commands with a treat. Start at
Raising Your Dog with the Monks of New Skete Here are more gentle ways of letting a little puppy know you are top dog:
''Elevation for small puppies: Sit on the floor and gently put your hands around your pup's middle, below his front legs, and lift him up. He is facing you. Hold him for 15 seconds. Repeat until he no longer struggles. If he is past 10-12 weeks, lift his front feet off the ground, but don't pick him up.
Cradling for small puppies: Hold your puppy gently on his back, as you would cradle a small baby. If he struggles, hold him firmly until he quiets for 10-15 seconds. With larger pups, you can do this as your sit on the floor, with your pup between your legs.
Quiet lying down: Place your pup on the floor on his side, with all 4 legs pointing away from you. Use your hands on his neck/shoulder area and middle, to hold him in this position. When he is quiet, praise him. Lengthen the time that you keep him quietly in this position. When he accepts this position well, handle his paws and muzzle, while keeping him quiet.''
The quotes mean this isn't my original work. It is copied from my Puppy Raising Manual. I have long used these or minor variations of them, and they are very effective. You may want to give him a belly rub while he is on his back too. Helps bonding. There is a big difference between him rolling over and demanding a belly rub, and you choosing a time to roll him over and rub his belly. The latter cements your place as pack leader.
Your puppy is much too young for a class, but not too young to start obedience. I start my 7 week olds on my way out of the kennel the day I pick them up. At that age, you must keep sessions short, only a couple of repetitions at a time. They learn very quickly then. Don't make the mistake of not obedience training a small dog. One of you will be in charge the next 15-20 years.