This same piece of advice was given to me by a vet when we got our Peter home. He is a green cheek conure and was about 3.5 months then. Honestly, we tried it, but it set us back instead of pulling us forward. Our little buddy just really needed time. He now is my cuddlebug, but he did take a while to get there.
Steps that worked for Peter and I were as follows. Got him to take treats through the bars (took a while!) Got him to take treats in the cage from pinched fingers then from the palm of the hand. Got him to come out of the cage for treats with big brother. Got him to step up for treats. This process took over a month of patience and effort. Our other l guy was stepping up day 1 (with nips...) Although the shy ones take a lot of time and patience we have found He is also a lot less nippy than the one who was bold from the start.
Not sure what your feeding your new Lil friend, but we have found that if they have a healthy diet then treats have a higher value and they are willing to do more to get them. Peter LOVED sunflower seeds initially so figuring out your birds treat of choice can be a big help. Not sure what Black capped conures prefer, our Lil green cheeks are partial to safflower and hemp seeds.
Don't sweat the bonding process too much, they come around in time.
