The factor that did not contribute to the rapid population growth in the United States in the early 1900s is:
More people moved from farms to large cities.
While urbanization was occurring, with more people moving to cities for various reasons, this did not directly contribute to the overall population growth in terms of increasing the total population. The other factors listed (greater immigration than emigration, higher birth rates than death rates, and advances in technology leading to cleaner food and water supplies) were significant contributors to population growth during that period.