Yes. Baptisms were frequently conducted within a few days of birth, sometimes the same day, and often state the age of the child, or the date of birth.
Catholic Church baptism records date from the 1500s (although not all still exist), civil records typically date from the 1800s, and in some places from the 1900s.
However, sometimes baptisms were performed much later, especially if the person converted to another religion. These do not necessarily state the person birthdate or age.