Her father, Emilio Cecchi (1884–1966), was from Florence, known for his work as a literary critic and author, but also as a film producer and director, while her mother, Leonetta Pieraccini (1882–1977), originated from Siena and was a well-known painter and writer.

Here, D’Amico's exposure to the film industry began as she frequented the soundstages, familiarizing herself with the processes, crews, writers, and actors.

Though Lele went into hiding during World War II due to his work for an anti-Fascist publication, the pair had three children who they themselves made significant contributions to Italian culture: Masolino, Silvia, and Caterina.

[11][8] With the war to come, d’Amico left the Ministry and became a translator of literary works, all the while being asked by her father’s peers to read scripts in order to give her feedback.

[13] Moreover, she proliferated during the time that Italian neorealism was being created and gaining global interest; she developed a style of writing that combined her literary education and understanding of the people, and was distinct for its succinct dialogue.