A new beginning for you both, exciting times. My advice follows the trend with allowing her to take the lead on interactions. They are great observers of surroundings and activities do grant her that time to get used to her new home, new flock (you and cats) new routines, new sounds, new food offerings it is a whole new world for her. Building trust before pushing step ups or other interactions letting her know she is safe and loved is very important. I think you will do great and no most Greys are not cuddle birds but a few are. I think you will find that like us each bird is a unique individual and this is an opportunity to learn who she really is, hint it may take mere weeks or it may take years to find out all about her. Greys can adapt to most situations if given the time and respect to make their own decisions about anything new including kids.