One man got down on his knees and kissed the rug emblazoned with the ship’s logo. Another lifted his wife and swung her around, ecstatic to be among the roughly 5,000 passengers to embark on the inaugural sailing of the world’s largest cruise ship, the Icon of the Seas.

For months, the 250,800-ton ship, which can carry nearly 8,000 people, has been making headlines — including some that have criticized its size and potential to damage the environment. But the passengers who plunked down $1,800 to $100,000 and boarded the ship at Port Miami in Florida on Jan. 27, said nothing could have prepared them for the vessel’s sheer scale.

“It’s stunning,” said Christina Carvalho, a 43-year-old accountant from Oakland, Calif., as she stood on the ship’s Royal Promenade, gaping up at “The Pearl,” a gigantic kinetic art installation. “It feels even bigger than I expected.”

While Royal Caribbean has packed the ship with amenities to craft “the ultimate family vacation,” the company’s design team has tried to defy negative stereotypes like crowded decks and long lines. Instead of steel walls, the interior is open and airy, with floor-to-ceiling windows to bring passengers closer to the water and make the central thoroughfare feel less like a shopping mall.

“Over the years our customers told us that despite being on the ocean, they did not feel connected to it, so with Icon we wanted to bring water everywhere,” said Jennifer Goswami, the director of product development at Royal Caribbean International.

I was on board the Icon of the Seas for five days of its seven-night inaugural sailing to the eastern Caribbean. Here are some of my takeaways:

Embarkation starts through Royal Caribbean’s app. After some glitches, it took me 10 minutes to scan identification documents, fill out a health form and pick a time slot for boarding.

On the day of the sailing, I headed to Port Miami expecting chaos, but as I got out of the taxi, I was greeted by a porter who took my bag and ushered me to the terminal. I scanned my app, showed my passport and went through security in less than 10 minutes. I lingered, waiting to see if others had as smooth an experience as I did, but there was just a steady flow of passengers ascending the gangway.

The ship has the feel of a city, with eight distinct “neighborhoods.” My favorite, Central Park, was filled with 20,000 plant species; it was the perfect place to stroll or read on a bench. The Royal Promenade, with karaoke and a piano bar, could get crowded and noisy at peak times.

The seven swimming pools are designed for different vibes and demographics: The Hideaway is an adults-only infinity pool, with D.J. sets and cocktails; another adult pool has an adjacent children’s splash pool. Empty lounge chairs were plentiful for sunbathers across the ship.

On our first sea day, I was so surprised by the relative absence of crowds that I walked the ship trying to find them. But with so many venues, including 40 restaurants, bars and entertainment spaces, passengers were constantly moving around.

Seeking a quiet space one afternoon, I found the Aquadome, a tranquil lounging area with wraparound windows. Fellow passengers napped there.

From a sunrise surf simulator lesson to late-night dancing in the nightclub, the ship seems to offer something for everyone, most of it free. The water park with six slides was a big draw. One ride, the Crown’s Edge, is not complimentary: Starting at $49, it tosses you (in a harness) above the sea, leaving you dangling.

There is a fitness center, jogging track, a basketball and soccer court, a putt-putt course, pickleball, rock climbing and dancing. A wellness center and spa offers treatments for an additional cost. All can be reserved on the app; for popular attractions like the Crown’s Edge it’s helpful to book ahead because places fill up fast.

For nightly entertainment, “Aqua Action” was a standout, with aquatic entertainers performing under a 55-foot waterfall, as was the comedy club.

Not surprisingly, some passengers felt overprogrammed. “There’s almost too much to do,” said Nancy Carter, 54, a nurse from Brighton, England. “It’s hard to plan your day and even when you are busy doing something, you feel like you are missing out on something else.”

At the Surfside neighborhood, there are pools and restaurants for both adults and children so that families can spend time together. For parents wanting alone time, the Adventure Ocean child-care facility has play areas and programs for ages 6 months to 12 years that is included in the fare.

There’s a social center for teenagers, too, with games and music. “It’s a great place to meet new people and make friends,” said Madison Foxx, 14, from Morrisville, N.C. Her mother, Ashley, a 38-year-old federal prosecutor, said the ship kept her two children entertained and allowed her both alone time and quality family time.

“I can relax and the kids are happy and busy all day,” she said. “Then we have many special moments together.”

One of the biggest surprises was the array of dining choices.

The Windjammer Cafe and the main dining room were the busiest all-inclusive options. My daily go-to was the Aquadome food hall, with crepes made-to-order and a Greek food stand. Another favorite of mine was Pier 7, a restaurant in Surfside that served raw-tuna Buddha bowls, mango-lime shrimp tostadas and other dishes.

Meals at specialty restaurants, such as Giovanni’s Italian Kitchen and Hooked Seafood, come at an additional cost, or are included in some food and beverages packages that range from $9.99 to $115 per day. Reservations are recommended.

The Empire Supper Club offers an eight-course meal paired with cocktails. At $200, the tasting menu included Wagyu rib-eye, rabbit and sea bass topped with parsnip and red beets.

Cabin prices — which recently increased, because of high demand — range from $2,699 per person for an interior cabin to over $100,000 for a three-story townhouse with an indoor slide and backyard. Some family accommodations have connecting rooms and large terraces.

Though only 204 square feet, my ocean balcony room did not feel cramped thanks to minimalist design and the views.

Royal Caribbean says it set a new standard for sustainability with this ship, installing advanced water-treatment and waste systems, among other features. But some environmental groups say that building a vessel this size is not compatible with the cruise industry’s long-term sustainability goals.

On board, I saw staff sorting through the trash to take out misplaced items to recycle, and single-use plastic appeared to be minimal; passengers were given reusable cups at drinking stations.

That the water slides remained on, even after they were closed to passengers, caught me by surprise. It seemed like an unnecessary waste of energy. (Royal Caribbean did not respond to a request for comment.)

Passengers I spoke to did not seem too concerned about the ship’s potential to harm the environment, with some arguing that land and air travel are not climate-friendly either.

Our seven-night itinerary started with two days at sea. The first stop was on Day 4 at Basseterre, the capital of St. Kitts and Nevis. Excursions ranged from a hike up Mount Liamuiga to a food-and-rum tour, with prices from $39 to $249. I chose a sailing and snorkeling excursion ($155) and enjoyed the secluded bay, but the beach was crowded and touristy.

An anticipated excursion for Ms. Foxx, the federal prosecutor, and others was Coco Cay, Royal Caribbean’s private island. When I asked about her visit — I called later, having to disembark before the excursion — Ms. Foxx said her children loved the slides and snorkeling.

And would she sail on the Icon of the Seas again?

“Yes, but I might wait a bit,” she replied. “I want everyone to get a chance to try it out.”