It really depends on the bird. It is easier to hand tame a bird that hasn't been tamed if you have a lot of patience and you don't get another bird. It took me 9 months to really gain Pretty's trust but some birds are longer and some are shorter. Some never tame it all depends. You will have to come to terms with that if they don't tame down.
It also depends what you mean by tame. Some people are perfectly happy if their bird runs up to the side of the cage and gives them kisses only others want their bird to cuddle on their shoulder with them what is your definition of tame?
If I was to get a bird that was not tamed I would sit and observe the birds and look for the one that comes to me when I click to it, looks at me and doesn't run, if I put my face next to the cage which one is not scared but curious, if I put my hand next to the cage what are the reaction.
I also had to get him clipped at least once so I could let him out of the cage without him harming himself.
If I had the time and would do it again I would work on clicker training my bird it helps trains them so much quicker, I have clicker trained my dogs but haven't had the time to do it with Merlin.