First, one needs to be geographically specific when referring to, "The Renaissance". When we study the history of "The Renaissance", we are essentially focusing on The NORTHERN Italian Renaissance, that is to say, cities directly to the NORTH of Rome, such as Florence-(The historic birthplace of "The Renaissance"), as well as Venice, Milan, Bologna, Pisa and Padua. It is important to mention this because it is directly related to the prior history of Italy, as well as to the earlier Medieval and Ancient periods.
One must remember that much of the Italian peninsula-(particularly to the NORTH of Rome), during much of the Medieval period, was at the Center of "The Dark Ages"; (in fact, it was a Northern Italian Renaissance Poet named Petrarch, who coined the phrase). "The Dark Ages" began almost immediately after the collapse of the (Western) Roman Empire in 476 AD/CE and lasted until 1050 AD/CE. Beginning in 1050, much of Northern Italy and Western Europe ushered in, "The Age of Scholasticism", which is a nickname describing The Late Middle Ages. If one examines this 1000 year historical period, you will notice that the Geography and peoples are nearly indistinguishable from the earlier Western Roman Empire. In other words, the lands and peoples of the Western Roman Empire, were the same lands and peoples of the Western Medieval period-(both during "The Dark Ages" and "The Age of Scholasticism").
When the "rebirth" of Classical Greco-Roman Antiquity took place, its Epicenter Florence, was the starting point of Northern Italy-(and perhaps even the starting point towards Northern Europe when seen from a South European or Mediterranean perspective). It was from Florence whereby, the Northern Italian regions of Tuscany, Lombardy and the Veneto helped to catalyze what would become The Northern Italian Renaissance-(1400-1600), or the birth of Modern Western History.
The reason why there was no "Renaissance" in the PRE-Modern History of Greece, was because of the fact that there was no "Dark Ages"-(unless you go back to the period before Homer, around 1100-800 BC/BCE or perhaps during the Slavic invasions of mainland Greece between 500 AD/CE-800 AD/CE. Though despite the Slavic invasions, the Greco-Byzantine Empire continued and even prospered). With these possible exceptions, there was no prolonged "Dark Age" within Ancient and Byzantine Greece. And since no prior Dark Ages existed in PRE-Modern Greece, there was no need for the renewal, re-cultivation or rediscovery of its earlier Hellenic roots and civilization. (It was actually when Greece was under Ottoman Turkish Muslim occupation for approximately 400-500 years that a quasi Dark Ages ensued, whereby much of Modern Greece was culturally distanced from the Western world and essentially forgotten about, as well as abandoned by the West....until the 1800's).
In the case of Italy, it was a different historical experience. The larger Italian ethno-racial group who inhabited much of the Italian peninsula in Ancient times, were the Romans. From the Italian peninsula, Rome went on to conquer several countries and peoples within Europe, North Africa and the Middle East. The Roman Empire, that is to say the Western Roman Empire, lasted nearly 500 years and collapsed into the Dark Ages for the next 600 years, only to be somewhat revitalized during The Age of Scholasticism for the next 350 years and then arriving at The Renaissance in Florence around 1400.
Italy's history has been a story of birth, advancement, decline, obscurity, a semi-reawakening, which resulted in a rejuvenation-(and furtherance) of its intellectual and cultural heritage. When examining the earlier years of Italy, one can chronicle and even chart the ups and downs, as well as the heights and plateaus of its historical lifespan. Such a timeline and charted map, made it possible for a Renaissance to occur, as well as distinct from the less historically elliptical lifespan of PRE-Modern Greece.