Yes, she could get citizenship under certain conditions. You need to address to a lawyer for the application.
Are children of Greek Golden Visa holders eligible for Greek citizenship?
My wife and I have been living in Greece on Golden Visas for a few years and recently had our second child here. Given that she was born in Greece, what kind of benefits is she eligible for? Can she get citizenship, rights to work and collect public benefits?
According to the provisions of Greek citizenship law in force, those children who have been born in Greece from third-country citizens, holders of a valid resident permit title and have attended a school that implements the Greek mandatory curriculum can apply for Greek citizenship from the enrollment in the first grade the elementary school. They are not eligible to apply if: when neither of the parents holds a resident permit or they hold only temporary resident permits; when neither of the minor’s parents have been living in Greece for more than five years with a resident permit, before the minor’s birth, nor have they been residing in Greece with a resident permit for more than 10 years in total, before and after the birth of the minor. A Greek citizen is entitled to all the benefits that every Greek citizen is granted, e.g., access to work, social benefits, etc.
The child needs to study in a Greek public school for nine years be issued Greek citizenship. It can also be a private school that follows the public educational system.
Children born in Greece have the right to acquire Greek citizenship when they go to elementary school.