Were the Roman and Greek empires around during the same time period?

The Greek and Roman Empire are identically different. The Greek one is older than the Roman since it was established by Alexander the Great at 323 BCE and lasted in the mainland of Greece until 146 BCE and the last remaining part of the Greek Empire Egypt until the death of Cleopatra Philopator the VII at 30 BCE. The foundation of the Roman Empire took place in the 1st century BCE with first Emperor Augustus between 27 BCE 14 AD/ CE.