Based on the provided options and the context of the Gold Rush, the most accurate inference about its impact on the city of San Francisco would be:
The mass migration of forty-niners transformed San Francisco into an economic hub practically overnight.
This response suggests that the influx of people during the Gold Rush significantly contributed to the city’s rapid growth and transformation into a major economic center. The other options either downplay the Gold Rush's impact or suggest behaviors that contradict the known history of many forty-niners staying in San Francisco after their initial attempts at mining.