Yes, a baby at zero months old is considered a newborn.
Newborn status typically refers to the period from birth up to around 2-3 months of age, though the specific definition can vary slightly. The term "infant" is broader, encompassing the first year of life (0-12 months). Therefore, a baby at zero months old falls under both the "newborn" and "infant" categories. In essence, the newborn phase is a subset of infancy.
This means a baby who is just born, or is in their first month of life, is accurately described as a newborn.