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. After that, they continued learning from their parents or went to school.
The Greeks loved games, especially games of challenge. They left time for their kids to play because they believed it was important to their minds, bodies, and growth. 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.