Final answer:
The child in the observation is in the sensorimotor stage, the first stage of Piaget's cognitive development, characterized by learning through senses and motor behaviors, and developing object permanence.
Step-by-step explanation:
Observing a mother and her newborn daughter, with the child looking at the mother's face and holding her finger, indicates that the child is in the sensorimotor stage of development. According to Jean Piaget, this is the first stage of cognitive development, lasting from birth to about 2 years of age. During this stage, a child learns about the world primarily through their senses and motor behaviors, such as grasping and looking. This stage is characterized by the development of essential cognitive abilities like object permanence, which is the understanding that objects continue to exist even when they cannot be seen or heard.