When do babies like to entertain themselves?

Hello my son is two months old and I'm trying to get him to be a little more independent We currently attend mommy baby cles but my son can't stand to be put down and cries to be held constantly. He has a tummy time mat and he won't have anything to do with it, he has a bouncer and hates it, he has a swing but only stays in for 5 minutes before he's screaming to be held. I always make sure he is fed, dry, and awake before I try to put him down so I know his needs are met. My question? Is this normal? When do they outgrow this phase? Literally can't do anything unless he's asleep and the sling kills my back believe me I've tried he is a heavy boy.