Congrats on your new Linnie! They are wonderful little birds. Your baby is still trying to get used to you after 3 weeks, it takes a while for them to settle in. Just be patient and don't try to rush things.
I have had 3 linnies including Napoleon (rip) and was a moderator of a Linnie forum and one common denominator amonsbt most linnies is they do not like hands. They don't like to be "pet". There are of course exceptions to the rule as with any bird. Mt Sampson is not afraid of my hands and while i can scoop him up with my hands when I need to, he grumps at me but is clearly not scared and just being a brat, lol. And he used to love scritches and being touched but preening is now rwserved for his brother. He is still an extreme cuddle bug who loves to sit on my chest abd give me kisses while i nuzzle him with my nose but doesnt want to be touched. Smooches on the hand is afraid of my hands, he will not step up and will fly away if he sees my hands. However he will allow me to kiss his beak andl fly to me and sit on my shoulder. So its not me he doesn't like, just my hands. I accept him for this and just modifiy how I handle him vs Sampson. Its just the way he is and he has been with me for 2,years now. Napoleon also didn't like hands but he was a rescue and came to me not tame so I don't know I'd he would have had he had a better life prior to me.
My point in all this rambling is that just give your baby more time to settle in and let himnset the pace. Your linnie may or may not like to be touched but if he steps up that's q great sign hands areent too scary. Unless you keep pushing to touch him. Rwpsect his boundaries and shown him he can trust you.
Each of my birds has different things they like and don't like.
Good luck with your new baby and let me know if you have anymore questions
Ps. Sorry for the typos, on my phone on the bus typing this