Great advice above by FaeryBee and looking forward to more updates. The most important part is recognizing that no budgie progresses the same in their taming/bonding and it's essential to allow him to initiate each progression so that you know he is comfortable with you. It sounds like he's well settled into his home now, but you will have to be very patient for him to get enough trust with your hand in the cage. As mentioned in the post above, don't try to move your hand any closer or anything until he can move around in the cage/play/chirp comfortably and etc. on his own without minding your hand. This could take weeks or longer~
Hope to hear more soon!
Hope to hear more soon!