Mr. Astorino — a former radio producer who, at 46, is a decade younger than Mr. Cuomo — has also shown surprising strength as a candidate in the past, handily winning a second term as county executive last fall, even though Westchester has more registered Democrats than Republicans.

Mr. Astorino has been the favored candidate of the statewide Republican Party establishment, having tapped Michael Lawler, the state party’s former executive director, to manage an exploratory committee. And on Wednesday, Republican officials seemed to be embracing their role as an underdog.

“Goliath, meet David,” said Ed Cox, the state chairman. “Rob Astorino has proven that a Republican can win in two-to-one Democratic New York. Rob has what it takes to reverse the decline of New York, not just try to manage it like our last three Democratic governors.”

Despite the seemingly long odds, Mr. Astorino’s early tactics appear to suggest several political avenues that could be potent. Mr. Cuomo has repeatedly tried to woo upstate voters, but support there has lagged. (Mr. Astorino will visit Albany, Rochester and Syracuse on Friday.)

The governor pushed for a major gun-control law that the State Legislature passed last year in the wake of the massacre at Sandy Hook Elementary School, and it has proved unpopular in more conservative, rural counties upstate. In his video, Mr. Astorino said the governor was “demonizing law-abiding gun owners” in New York.

Likewise, Mr. Astorino seems intent on making an issue of hydraulic fracturing, the gas and oil extraction method known as fracking. The process is effectively banned in New York, and Mr. Cuomo has been accused of stalling on the issue by awaiting a long-simmering report from his Health Department. That accusation was echoed by Mr. Astorino in his video on Wednesday, in which he said the natural gas industry could “lower electric rates, improve air quality, create tens of thousands of new jobs and billions in new revenue.”

“But,” he added, “Governor Cuomo sat on his hands for four years and refused to make a decision.”

Mr. Astorino, who lives in Mount Pleasant, N.Y., with his wife and three children, was a radio host for the Catholic Channel, a SiriusXM satellite radio station, and helped to start ESPN Radio in New York over a decade ago. As a fluent Spanish speaker, he capitalized on his popularity among Latino voters when he was first elected county executive, in 2009.