The original Latin village was probably founded in the 9th century BCE, but may have been an outpost as early as the 10th century BCE. So it’s likely to have been built gradually over the course of 100 years. Even if there had been a concerted effort to transform it from an outpost into a village, however, it still would have taken a few months to make it more than a very basic settlement. Furthermore, the Republic wasn’t created until 509 BC, which would be somewhere between 300 and 400 years later. And of course, the city is still being developed to this day. That’s why it is sometimes called “the Eternal City.”
Note: I am using modern archaeological estimates rather than the dates proposed by ancient Roman historians (who believed the city was founded in 753 BCE).