At noon, Seattle’s Westlake Park bustles with business professionals lining up at gourmet food trucks, tourists clutching shopping bags who flow to and from stores like Nordstrom and Zara, and others playing with oversized chess pieces scattered throughout the space.

But peer through a pair of bronze binoculars placed on a pedestal at the center of the plaza, and you’ll see a much different Seattle: an image of that very spot 53 years earlier, when only one major building stood here.

The installation, conceived by urban planner and landscape designer Erica Bush, captures the mood in Seattle, where residents and local leaders alike are grappling with the rise of unprecedented prosperity and severe inequality.

“Seattle in some ways wants to remain a small town,” says Ms. Bush, who created the art installation as part of Seattle’s Design Festival. “It’s struggling to figure out how compassion fits in with the major influx of money.”

The Emerald City stands at a moment of roaring success. Construction cranes pepper the skyline, creating offices for Amazon, Facebook, and Google. Median household income grew faster here than in any of the 50 most populous American cities last year, according to the Census Bureau.

Yet that means that fewer middle-class families can afford to buy or rent. Historically black neighborhoods dwindle as residents are pushed to cheaper suburbs. And in November 2015 Seattle Mayor Ed Murray declared a homelessness state of emergency after a 21 percent rise in the annual count of people without shelter, to nearly 10,000.

In the city that gave birth to grunge, where lumberjack flannel reigns, many worry about its soul slipping away. They fear growth will push out all but the extremely wealthy and the city will awake as “the next San Francisco,” a tech-dominated metropolis where middle-class dreams wither.

“From the time Seattle was founded, it’s always been looking at San Francisco as both something to compete with and as a cautionary tale,” says Fred Moody, author of “Seattle and the Demons of Ambition,” a chronicle of Seattle’s recent history.

Other prosperous cities in the United States, from Atlanta to New York, face similar equity gaps between haves and have-nots. Yet Seattle faces a particular challenge to its self-image as a progressive city where anyone can thrive. So Seattle’s mayor and city council have launched a battery of liberal policy experiments, from the nation’s first $15 minimum wage in a major city to a law requiring landlords to rent to the first qualified applicant to avoid discrimination.

The experiments, on some level, are a sign of desperation – the desire to add some humanity to the march of the free market and maintain some level of inclusiveness of the less well-off in its policy and character.

Yet running beneath are shoots of optimism within the city that the experimentation – coupled with the passion of young people drawn to Seattle’s progressive reputation – could make Seattle a pioneer in solving these problems.

“The amount of activism and civic engagement is at an all-time high here in Seattle,” says city Councilmember Lisa Herbold. “And that’s really the thing that will give the prevailing wisdom about us losing our soul a run for its money.”

Soul-searching in Seattle

This fall, at a gathering to discuss the challenges and opportunities of the “Region of Boom,” concern over newcomers loomed large. In 2014, nearly 65,000 individuals from out of state earned Washington State driver’s licenses in Seattle’s King County, shattering the previous high mark set in 1990 at the height of Microsoft’s hiring spree.

Samuel Assefa, director of the city’s Office of Planning and Community Development, called on locals to embrace newcomers like him, pointing out surveys that show many people move to Seattle for the lifestyle and values before finding work. Data presented by Seattle-based land conservation group Forterra showed newcomers are more likely than their peers who grew up in the Northwest to identify themselves as environmentalists, and believe affordable housing is more important than beautiful housing.

“I don’t see heartless gentrifiers in that data,” said Forterra government affairs director Lena Chahim.

Playing off the chasm longtime residents can feel between themselves and new tech workers, The Seattle Times started an occasional Q-and-A with Seattle newcomers. In a recent column, Amazon employee Varsha Raghavan said she and her co-workers pursue more diverse interests, such as acting and music outside work, than others assume.

“I understand where the negative stereotypes are coming from: ‘The tech bros are coming, they only care about themselves, they’re going to destroy our culture,’ ” she wrote. “I understand the concerns – the community getting broken up and gentrified. I empathize with that but ... it’s important to recognize that Amazon employees, regardless of whether we’re native Seattleites or not, want to contribute to our community.”

Indeed, there’s a strong community ethic.

“What I sort of love is that we never miss an opportunity to tax ourselves, like taxing public transit, we’re super into that, passing levies for schools.... The average Seattleite understands their responsibility to their fellow Seattleite,” says Nate Berends, a concert and event producer from the East Coast who attended the “Region of Boom” conference.

Others there raised concern about the city’s growth disproportionately hurting African-American and Hispanic communities. “Growing up in Seattle, I’m seeing a lot of changes, a lot of loved ones, friends, being pushed out,” said Jill Mangaliman of advocacy group Got Green, pointing to data showing the population of Seattle’s Central District dropped from 73 percent black in 1970 to 19 percent black in 2014. “It’s a brown doughnut, where all the communities of color are being pushed out.”

Fueling the boom

Nothing takes the blame – or praise – for Seattle’s growth more than Amazon, its largest private employer with 20,000 people in Seattle, 15 percent of whom live within the same ZIP Code as company headquarters, according to company statistics.

Unlike other area juggernauts like Microsoft or Boeing, located in suburbs, Amazon is headquartered in urban Seattle.

“The growth is being driven by Amazon and they’re right in the heart of downtown,” says Michael Luis, a public affairs consultant and author of “Century 21 City.”

The company already transformed the former industrial zone of South Lake Union into a trendy neighborhood when its first city campus opened in 2010.

Outgrowing that, Amazon is now building a new downtown campus, complete with giant glass spheres, which will provide a place for employees to wander through exotic plants during breaks.

Including the new downtown campus, Amazon stands poised to occupy one-fourth of Seattle’s market inventory of premium office space, with room for 55,000 additional employees (about 8 percent of Seattle’s current population).

Other technology companies feed off Amazon’s boom. Silicon Valley giants Google, Facebook, and Apple have opened or are building new Seattle offices. Seattle-based data visualization company Tableau Software bought more buildings to expand its city footprint. Expedia plans to move its headquarters from suburban Bellevue, Wash., to Seattle by 2019. The number of technology-related jobs in King County rose 56 percent between 2005 and 2015, from about 88,000 to nearly 138,000 jobs.

Success with equity

While growth propels Seattle to the top of many top 10 lists, it also prompts worries about the people it left behind. A half-mile away from the “Region of Boom” conference, activist Xochitl Maykovich of the Washington Community Action Network organized local residents to tell city council members of their inability to pay steep upfront costs for Seattle rentals.

A November report showed that Seattle led the country in fastest home-price growth – 11 percent – out of 20 major metropolitan regions over the past year (September 2015 to September 2016). Rental prices are similarly rising. Ms. Maykovich succeeded in lobbying the city council to limit those upfront deposits, requiring security deposits to cost no more than first month’s rent, and allowing renters the right to pay move-in costs in installments.

“The idea that we let the market just take care of things and let Seattle become a playground for the rich is at its core unfair,” she says. If people with jobs in Seattle can’t find affordable housing there “that’s essentially going to force people with lower incomes to move out of the city and then have two-hour commutes to get to their jobs. When that happens you’re taking away parents from their kids, you’re contributing to the ridiculous traffic we have in Seattle.”

Seattle voters recently passed a $290 million housing levy in August, double the amount that voters last approved in 2009. The levy will build or preserve at least 2,150 units of affordable housing and provide emergency rental assistance to at least 4,500 families, according to the city.

City council members are also considering measures to reach out to the growing homeless population – including providing trash services at homeless encampments. Mayor Murray recently released a comprehensive homelessness plan geared around moving people directly into housing rather than transitional shelters.

“Seattle is on the front cutting edge of a city that sees the problem and is trying to come up with housing and solutions,” says Al Levine, a professor at the Runstad Center for Real Estate Studies at the University of Washington and former deputy executive director of the Seattle Housing Authority. “We’re far and away the most supportive city in the country for local dollars on housing.”

Not everyone is on board with the city’s liberal laboratory. Landlords and many residents reacted strongly against the first-come renter’s law, which was scheduled to take effect Jan. 1. The city’s homelessness proposals draw critiques.

“Seattle, frankly, needs adult supervision,” said Republican state Sen. Mark Miloscia at a September press conference after an out-of-control driver killed a homeless man camping next to Interstate 5.

“This is lawlessness!” he said of Seattle’s consideration of allowing greater protection for homeless encampments. “I believe it will attract tens of thousands of people to our state, and our jungles will get even worse,” he said, referring to a longtime homeless camp underneath I-5 known as “The Jungle,” which the city cleared in October.

Residents with perspective on Seattle’s history interject some calm into the angst over Seattle’s future. Seattle has survived major booms and busts before – from the 19th-century Klondike Gold Rush when the population of Seattle nearly doubled in a decade to the 1960s Boeing bust that caused enough people to flee town that a billboard went up reading, “Will the last person leaving Seattle – turn out the lights.”

“It may just be because we’re such a young city, or it may be something kind of exceptional about Seattle and its natural settings, but this boom and bust cycle is really the one constant in our history,” says Mr. Moody. “It seems to me that each boom looks bigger than the last because the city is bigger.”

The explosion of Microsoft and influx of rapid wealth created a major shock in the 1980s and ’90s that in some ways caught people more off guard than today’s Amazon boom, says Mr. Luis.

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“Seattle up until the mid-1970s was kind of a Podunk place,” he says. “It was only about 10 years later that you suddenly had this transformation and there were a lot of people very uncomfortable with that. Now, a couple decades beyond that, people are getting comfortable with it.”

“Seattle still maintains its basic underlying culture,” says Luis. “It doesn’t feel like San Francisco here, it doesn’t feel like Los Angeles, even though it’s full of people from San Francisco and L.A. [Seattle] still kind of maintains that weird, funky, moldy, upper-left-hand-corner sense that it always had.”