Classical Greece came before the Roman Empire. The Classical period of Greece is generally considered to have lasted from the 5th to the 4th century BCE. This era saw the rise of city-states like Athens and Sparta, and it was a time of significant cultural and intellectual development, including the works of philosophers like Socrates, Plato, and Aristotle.
The Roman Empire, on the other hand, began much later. The traditional date for the founding of Rome is 753 BCE, but the Roman Empire itself didn’t begin until 27 BCE when Augustus became the first Roman Emperor. This means that Classical Greece predates the Roman Empire by several centuries.
In summary, Classical Greece flourished first, and its cultural and intellectual achievements laid the groundwork for much of what would later be developed and expanded upon by the Roman Empire.