Miami (CNN) The first U.S. cruise ship bound for Cuba in decades set sail Sunday as salsa music played and protesters picketed nearby.

Standing beside a Cuban flag and an American flag, the cruise manager touted the journey as "the beginning of a new era."

A photo posted by Annie Rose Ramos (@annieroseny) on May 1, 2016 at 1:27pm PDT

But not everyone was happy about the new route.

A small group of protesters gathered outside the port Sunday. And as the cruise ship was getting ready to leave Miami, police descended upon a nearby boat labeled "Democracia," where demonstrators held a blue sign that said, "Castro why do you ask Cubans for a Visa to visit their own country?"

A photo posted by Annie Rose Ramos (@annieroseny) on May 1, 2016 at 12:44pm PDT

The demonstrators didn't stop the cruise ship from pulling out of the port.

Putting politics behind as ship heads toward Havana

About 700 passengers are aboard the ship, operated by Carnival Corp.'s Fathom cruise line.

Some of those passengers said they don't want politics to interfere with the historic occasion.

As she waited to board, Pam Carlson said she wanted to put politics behind and travel to Cuba for the people.

"My grandmother went way back in the day, before it was ever closed, so just to be able to go there and meet the people and see the people, it will be meaningful to us," she said.

Gary Carlson said to him, the controversy surrounding the cruise doesn't add up.

"I'm not sure I really understand, because it's time to put those things behind us," he said. "Really the big issue is government to government, not people to people, and that's what we're excited about participating in."

Salsa, cigars

The seven-day cruise is scheduled to stop in three cities: Havana, Cienfuegos and Santiago de Cuba.

Scheduled activities on board highlight Cuban culture.

Garcia Baxe, 49, is a dance instructor on Fathom Cruise's first trip to Cuba from Miami. Born in Angola, Baxe will teach salsa and cumbia to passengers headed to Cumbia so they can "integrate into Cuban culture better" during their trip. A photo posted by Annie Rose Ramos (@annieroseny) on May 1, 2016 at 11:29am PDT

As the boat sailed, a salsa band serenaded passengers on deck.

Jesse Mercado, a business owner from Los Angeles, was one of the first to hit the dance floor with his girlfriend, putting aside the small American and Cuban flags that they had been waving at people on the shore as the ship passed by Miami's South Beach.

He said he was looking forward to buying some of the island's famed cigars, but he "most likely" wouldn't try to bring them back to the U.S., where an embargo on Cuban-made products still exists.

"I'll probably smoke them all there (in Cuba)," he laughed.

Jesse Mercado, 51, from Los Angeles eager to get his dance moves on who is most looking forward to purchasing cigars in Cuba. He is a construction manager back home. A photo posted by Annie Rose Ramos (@annieroseny) on May 1, 2016 at 1:40pm PDT

Retiree Carl Harbour sat watching fellow passengers dance to the music as the boat left Miami's port, looking on as others posted selfies. When asked what he most anticipated about arriving in Cuba, he smiled and said he, too, was looking forward to a cigar.

"When I got old enough I acquired a taste for Cuban cigars so I have come to appreciate Castro trying to help the common people all these years," he said.

"I don't think he is one of these dictators who keeps his money stocked away in some Swiss bank account. I think he really wanted to help the people and improve the life of the common people of Cuba."

Cruise almost didn't happen

The historic voyage -- the first U.S. cruise bound for Cuba in nearly 40 years -- almost didn't happen as scheduled.

Last month, controversy erupted over a Cuban law that prevented Cuban-born passengers from coming to the island on boats. The law stopped Fathom owner Carnival Corp. from selling tickets to Cuban passengers.

However, the two plaintiffs, Cuban-born Americans Amparo Sanchez and Francisco Marty, were not on board the ship, their lawyer, Javier Lopez said, "not because they don't want to be but because the Cuban government requires people that were born in Cuba to jump through a whole bunch of other hurdles."

He explained that the couple would have had to go to the Cuban embassy in Washington, D.C., which opened last year, and "get the most expensive passport in the world.

"Then good luck if you get it, then you can get in the boat."

Cruise officials say six of the passengers on this week's cruise are Cuban.

Beatriz Melendez is one of them.

The 52-year-old was 4 when she left Cuba with her sister and parents. Now, she and her sister are taking the cruise to Cuba together.

A photo posted by Annie Rose Ramos (@annieroseny) on May 1, 2016 at 2:21pm PDT

As the cruise ship left the port in Miami, the sisters spotted a rainbow spanning the bright blue sky -- a sign that the spirit of their parents is with them, Melendez said, as they begin their journey back home.