The Roman Empire began with Caesar Augustus, the first Roman Emperor, in 27 BC.
Formally maybe, but the conquest of Ostia was the lowly beginning of the Roman Empire. It became more convincingly an empire with its conquest of Italy and the early-3rd century defeat of Carthage and Roman annexation of its European territories.
There was never a Roman Republic, there was a bunch of mafia-style crime families that ruled as an oligarchy.