The survey found that 41 percent of respondents favored diplomatic engagement, followed by 35 percent saying it should be easier for Cubans to migrate to the United States.
"We presented 10 different policy measures, and the respondents can choose as many as they want," said Cesar Melgoza, CEO of Moxy.
"The one that was chosen most often, overall as well as by Republicans and Democrats, was diplomacy," added Melgoza.
The polling results come as the Biden administration is expanding its diplomatic footprint in Cuba. The State Department last month allowed diplomats on the island to be accompanied by adult relatives, but the White House has stopped short of the policy of rapprochement from the Obama era.
Meanwhile, Cuba remains in the political spotlight, particularly in Florida after protests on the island renewed interest in supporting the Cuban opposition among some US groups.
But according to Moxy's poll, Americans overall don't see Cuba as a top issue.
On a scale of 1 to 5, Cuba received a score of 2.74 as a policy that affects how respondents vote.
Among Democrats, the average score was 3.01 and among Republicans it was 2.67.
Cuban-American voters were most likely to have their vote swayed by Cuba policy, with an average score of 3.75.
Former Rep. Joe Garcia (D), a South Florida political veteran, said the poll results indicate a need for US President Joe Biden to engage more in Cuba policy.
"I'll go so far as to say that if he does not, he will have missed a premium opportunity to endear himself to the Cuban people in South Florida, perhaps to impact the next election," said Garcia.
"I don't know what his advisors are thinking. From my point of view, it's the perfect opportunity, and it's harmonic with democracy. It's harmonic with human rights, it's harmonic with the best political strategy. So there's no reason not to pay more attention," he added.
According to the poll, 24 percent of respondents think Biden proactively represents the interests of the Cuban people.
That puts the president behind Sen. Marco Rubio (R-Fla.), at 29 percent. But Biden is ahead of Rep. Maria Elvira Salazar (R-Fla.), at 17 percent, and Sen. Ted Cruz (R-Texas), with 15 percent.
Although Republican politicians dominate the list of individuals who represent the interests of the Cuban people, almost 37 percent of voters said Democrats best represent Cuban Americans, and nearly 27 percent of voters said Republicans do.
Garcia interpreted the poll results as an invitation for Biden to engage Cuba with a "carrot and stick" approach.
"And frankly, invite those Republicans who are most outspoken on the issue into the dialogue, because otherwise they'll criticize probably anything he proposes anyway. But bring them in into it, make them part of the team, come up with a plan. And more importantly, do something about it," he added.
The poll was conducted online Aug. 2-9, with 1,014 completed responses and an oversampling of Cuban-origin voters.