Answers
Your family members have to first apply for long-term residence permits after 5 years of permanent and legal stay in Greece. In the case that your 3-month-old baby was born in Greece, it is subject to other legal provisions for citizenship.
In order to obtain a long term citizenship, there are multiple procedures applicable, depending on the labor activities of the applicant.
In order to apply for citizenship, you must have at least seven years of residence in Greece. Before that, you cannot apply.
Greek Golden visa is a qualifier for the European residency. The visa is granted for five years and renewed every five years if the property investment is retained. It is not necessary to live in the country in order to retain and renew the investor visa. However, citizenship can only be granted after seven years of residency.