The baby will get a residency permit as a family member. But if he/she grows up and live in Greece for more than seven years, goes to a Greek school or learns Greek, then your child would be entitled to get citizenship.
What kind of resident permit does a newborn baby of a Golden Visa holder in Greece receive?
If my wife and I obtained our Greek resident permits through the Golden Visa program and our child is born in Greece, is the baby entitled to Greek citizenship by birth or just a resident permit?
You must apply for your minor child with all the supporting documents. The minor child is definitely and with no doubt entitled to get the permit. A birth in Greece doesn't directly give the right to Greek citizenship. Other conditions have to be met, the most important and essential being to have lived a number of years in Greece and to have followed some years at least of Greek education.
According to Greek citizenship law, a child of third-country citizens who is born in Greece by parents who live permanently and are legally residing in the country for at least five consecutive years has been granted Greek nationality since birth, provided that his/her parents submit a joint declaration and application for registration of the child in the municipal register of his permanent home within three years of the birth. In cases of a subsequent submission of the declaration and application, citizenship shall be obtained from their submission. If the child was born before the five-year legal stay of both parents in the country, the joint declaration and application form is submitted with the expiration of the five-year legal residency of both parents, and the child acquires Greek citizenship from their submission. So, since you are granted for permanent resident permit as property owners, you keep a title of residence to live legally in Greece. According to the above provisions, your child, born in Greece, could acquire Greek citizenship after the five-year legal stay of both parents in the country upon application.
Following my previous answer and according the recent amendments of Greek citizenship law, a newborn child from third-country citizens in Greece is granted Greek citizenship if one of his parents has legally resided in Greece for at least five years and upon certificate of the child’s enrollment and attendance of the first grade of elementary school. Documentation to be submitted upon application: declaration – application for acquisition of Greek citizenship; Greek municipal birth registration; marriage certificate of the parents, authenticated and translated into Greek, or, if the marriage took place in Greece the municipal marriage registration; parents’ resident permits; passports of the parents, officially translated; certificate of the child’s enrollment and attendance of first grade of the elementary school. The time of application is from the enrolment in the 1st grade of elementary school. So your child is granted a resident permit through your investment in property and could be granted citizenship as above.