Screvane's service to New York City started when he turned 22, when he took a job as a garbage truck driver.

His uncle, a former employee of the New York City Department of Sanitation, encouraged him to pursue the position.

In consequence, though the cost of hiring trucks was significantly reduced, after each snowfall, the cleaning and dyeing bills increased substantially, as bystanders' clothes would be splattered by passing cars.

On September 7, 1961, he defeated State Senator Thomas J. Mackell in the Democratic primary for the position.

During the Democratic primary, he came in second to Abe Beame, who eventually lost the election to John Lindsay.