How long does it take for a baby to self-soothe?

My 3wk old doesn't seem to fall sleep, unless I'm holding him and nursing or he's in his carseat. Sometimes he falls asleep on his own, but most times he's near me. Once he's sleeping I try to put him in his crib or lay him down near me and it's good for about 15mins, until he realizes that he's not being held or nursing anymore. And I have to re-soothe him (most times with my nipple in his mouth). I try the pacifier, but when he's awake and it pops out of his mouth, he'll start crying. He's only 3wks old, so I don't expect much, but it's hard to hold him all the time, becuase I have to eat, pee, shower, etc. Does anyone have any suggestions for me? Besides a SLING.