Is expiation (kaffarah) or making up the fast (qada') obligatory for a girl who reached puberty during Ramadan and broke her fast one day at the beginning of her fasting by eating cookies?

You must repent and make up for the missed day without expiation, as expiation is specific to breaking the fast through sexual intercourse. For delaying the make-up fast, the majority of scholars stipulate feeding a needy person one and a half kilograms of rice, unless the delay was due to ignorance of its prohibition, in which case nothing is required.