Newborn puppies need to be stimulated to excrete waste (pee/poop) for the first few weeks. The mother would normally lick the puppy which would cause the puppy to poop. Since the mother is absent try wiping the puppy's genitals with a cloth dampened with warm water.
That should stimulate the puppy. Just make sure you're prepared for what might be a bit of a mess. Make sure you clean both the puppy afterwards as well as the area and your hands or anything else that comes in contact with fecal matter or urine.
You may have to continue doing this for a couple more weeks or so.