When i brought my two boys home i left them in their cage for one hour,they had quite a long journey.I then let them out to familiarize with their play stand & surroundings.It is a good idea for perhaps the first week or so to have the perches in the cage near
the middle & bottom,maybe an old towel or blanket with some newspaper on top, changed daily, this will cushion any falls your grey may have.Baby greys love scratching on the bottom of the cage so dont be alarmed if your baby does this, it will pass.
Greys love routine, so start as you mean to go on.Where your grey is going to have breakfast,what times she is coming out of her cage etc,,they can adapt & obviously there the routine is flexible but try to stick with it.
Im sure you will be fine & your baby will fit in with your lifestyle, keep us informed