My Claude wouldn't allow me to pick him up when I first got him. He would run away even if I walked over to him. He would sit besides me, though. From sitting, I would pick him up and stand up holding him (which I had to do tight), most every day, for a few seconds. I would talk to him and tell him what a good boy he is. I extended the time, gradually, to about a minute. Slowly he got over it. He doesn't like to be picked up, but he does let me, for necessary reasons. It took about a year. He doesn't run away when I walk over to him anymore, either.
I have another cat, Ariel, who I can't pick up. I can hardly touch her. I've had her a year and a half now. Even she has gotten better at letting me walk over to her and touch her. But, it is a very slow process. I have hope, still.
The first year I had Claude I fed him with his food dish pushed to the back of the open carrier - so he'd have to go in to eat. I was afraid if there was a medical emergency, I wouldn't be able to pick him up to get in the carrier, so I would be able to coax him in with the food (he's food obsessed). But that wouldn't even work with Ariel. I had to hire someone to help me get her into the carrier to take her to the vet for shots (No kidding!)

We used a towel, but still the helper was scratched good. She's a hissing, yowling, monster if you try to pick her up. I'm sure she would bite if she could. I don't know what I'll do if I ever have a medical emergency with her. I just hope I don't
Robin