Have you got anything else that he is already familiar with, to pick him up? Like a multi-stem perch that he's used to in his cage (that's what I taught my then untame Amazon to step up on), or folded rope perch (that's what I ask Kobe the Pionus to step up on), or basket handle, or cushion, or the top of a travel cage, etc?
Think about the consequence of your actions too... if you go up to him, pick him up and put him straight back into his cage, it sounds like it is not reinforcing to him, when he would rather be out on the floor. I would wait until he is calmer/more receptive before picking him up. Then when you put him in his cage, make it wonderfully reinforcing so that he'll more likely choose to do what you ask next time.... have a new toy waiting in there for him, a fresh food bowl, loads of praise or even a treat if he would take it... whatever is reinforcing for him, the individual.
Right now, he has learned that if he bites, your hand goes away. Trouble is the longer he bites in that scenario the behaviour is becoming more ingrained. So see what you can do to diffuse the situation first before picking him up. Maybe ignore him until he is calmer.
It would be good when he's relaxed and receptive to start teaching him to step up on a perch of some sort for times like this. With Kobe I used to ask him to step up on the folded rope perch each time I took him out of his nightcage. I chose a rope perch as he was used to them in both his cages. Reinforcement was coming out of the cage in the morning. We did it so often that he doesn't question it now. But you may have to desensitize your bird to the perch (getting him gradually used to the sight of it) before teaching him to step up onto it in tiny manageable steps.
