So this is a tricky question to answer because much of Rome's very early history is shrouded in myth and legend.

Roman historians and poets attempted to pin-point various timings for Rome's development. Livy talks of inter tribal warfare still occurring around the time of the senate being installed, and claims that under Tarquinius Priscus, the legendary 5th king of Rome, walls and sewers were constructed. This was around 600-580 BC.

Again, this period of Roman history comes to us in myth, as it did to the Romans writing 2000 years ago. There is no exact date, as over this period the seven hills began to be settled.