When a baby was born in ancient Greece, it was a cause for celebration. The Greeks loved dance. So of course they had a dance the father did, holding his new baby. The mother made a wreath for the door so everyone would know they had a new baby. Friends and family brought gifts.
Sparta was the exception (of course.) When a baby was born, it was looked over very carefully. If the child was not perfect, it was killed. The Spartans had no interest in raising a child who was not physically able to become a great warrior.
For those families who did not have slaves to do all their work, even toddlers helped in the fields. Until age 6, nearly all children, boys and girls, were taught at home, by their mother.
There was time to play. Kids played a game similar to basketball. They had little carts they pulled around. They loved games of skills, like tossing sticks into buckets. They listened to stories, fables, and legends.