I know it is necessary for your beliefs to pretend that ‘father’ does not mean ‘the man whose sperm united with the mother’s egg to create the person’.However, reality doesn’t really give a stuff about your beliefs.
Well the law does does give a stuff which is why adoptive parents and non-biological parents are rightly on a child's birth certificate.
Man A cuts the baby's cord, holds her, comforts her, baths her, dresses her, changes her nappies, prepares her meals, helps her with her homework, gives her advice, and unconditionally loves her.
Man B donated the sperm so the baby can exist.
Which man is the baby's father?