Jordan Morris added a goal and contributed on three others, Josh Sargent scored and Christian Pulisic converted a penalty for the Americans, who also benefitted from an own goal by the Cubans.
McKennie put the hosts in front less than a minute into the contest off a low cross from Morris.
He added a second off an almost identical play in the fifth and after setting Morris up for the hosts' third goal in the ninth, completed his hat trick in the 13th.
It was the fastest known hat trick ever for the USA.
It was a second big defeat in the competition for Cuba, who fell 6-0 to Canada in the previous round.
While Gregg Berhalter's United States will need to show they can beat much higher quality opponents, the easy win was a welcome confidence builder for a team that lost to Mexico in the Gold Cup final in July, then lost to Mexico again in a friendly before playing to a 1-1 draw with Uruguay last month.
Modeled on UEFA'S tournament of the same name in Europe, the Nations League offers the United States and other CONCACAF teams a chance to boost their world rankings to earn automatic entry into the final round of qualifying for the 2022 World Cup.
The tournament is also the qualifying path for the 2021 CONCACAF Gold Cup.
The United States — still rebuilding after failing to qualify for the 2018 World Cup — are among 12 teams in the tournament's A League.
In other A League action on Friday, Mexico beat Bermuda 5-1 in Hamilton.
Jose Macias scored twice and Uriel Antuna, Hirving Lozano and Hector Herrera scored for Mexico, with Nahki Wells grabbing the lone goal for the hosts.
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