I hate to sound negative here but this probably isn't the best time to bring a big bird into your home. Big birds just require an extremely stable environment. You have to adapt YOUR life to fit big bird's natural needs and behaviors, because they can never really adapt to people's needs for a special routines and lifestyles, especially sleeping baby schedules. Your girlfriend would need to be prepared to change her lifestyle and make sacrifices to ensure the bird is given the best environment - my guess is the baby is going to be first on her priority list - as it should be. Disruptions, lack of proper attention or insufficient committment to training to preventing undesirable behaviors can ruin your bird's opportunity to bond with you and give him/her a really poor outlook moving forward.
I would not say that Eckies are good begginner birds, simply because of their diet issues, sensitive, more laid back, observant and easily distraught natures which can all lead to unfortunate birds that pluck, chew or have worse issues - too many people get frustrated if the bird they gets becomes a plucker or self mutilator and they end up going from home to home or shelters.
African Greys are much quieter birds, but also extremely sensitive and can be one person birds. Jealousy of a new baby or having the bird hold a grudge if it feels it has been neglected could also result in plucking or fearful behaviors.
Macaws are just not great birds to have with a baby in the house - period. I ADORE my Macaw, but let me tell you - he screams when he needs to and can be heard several hundred feet away with the windows closed. They ALL scream - any Macaw that does not scream is either sick or a stuffed animal in a toy store. We knew this when he came home to our house and have adjusted our lives to live with screaming. Good luck making that work with a sleeping baby and still have a bird without major problems.