CHICAGO—Former President Barack Obama, once a community organizer, has gotten a taste of community organizing himself as preservationists and other activists have slowed the construction of his presidential center.

The groundbreaking for the center to celebrate Mr. Obama and press its mission of fostering future leaders could finally happen late this summer after years of lawsuits, fundraising and federal reviews. The eventual opening, previously scheduled for 2021 before the challenges arose, is poised to set a modern record for time between a presidency and completion.

While many of Chicago’s political and business leaders have embraced the center, some activists have tried to stop construction, and others have sought to stake a claim for a piece of the economic windfall it is expected to generate. They have protested outside government meetings, organized petition drives and appealed a case to the U.S. Supreme Court.

Presidential libraries opened in recent decades have done so in about half the time as what is expected for Mr. Obama’s center, Wall Street Journal calculations show. The Ronald Reagan Presidential Library welcomed visitors just more than 1,000 days after Mr. Reagan’s last day in office. Bill Clinton’s took 1,398 days. Monuments to George H.W. Bush and George W. Bush averaged 1,653 days.

It is likely the Obama center will open more than 3,100 days after the 44th president left the White House if construction starts in early September and takes no more than the four years now estimated.

The project’s urban environment created complexities, as has Mr. Obama’s 2016 decision to locate the center in a park listed on the National Register of Historic Places. The site, near the Museum of Science and Industry, triggered multiple federal reviews and legal challenges.

“Because it isn’t in a green-grass site or on a huge university campus, the level of community engagement was much more intense, as it should be,” said Valerie Jarrett, a former senior White House adviser who is president of the foundation overseeing the project.

A rendering of the public plaza and museum building on the campus.

A rendering of the public plaza and museum building on the campus.

Photo: The Obama Foundation

Ms. Jarrett noted that Mr. Obama worked as a community organizer in Chicago during the earliest stages of his career and that he wanted guidance on the project from those who live and work in the surrounding area. “The design of the campus is better today with the benefit of community input, so the time was well spent,” she said.

The center’s proposed location on Chicago’s South Side is near the University of Chicago, where Mr. Obama taught constitutional law, and just north of the neighborhood where former first lady Michelle Obama grew up.

The roughly $700 million campus is expected to include a museum, Obama Foundation offices, a public library and recreational space. Besides the usual trappings of a presidential museum, the foundation also plans to offer regular programming that it says will help train a new generation of leaders to “change history once more.”

The development is slated to occupy about 20 acres of the more than 500-acre park and is projected to attract as many as 750,000 annual visitors. The Obama Foundation and Chicago leaders hope the project will transform its surrounding lower-income neighborhood.

Jackson Park is listed on the National Register of Historic Places.

Jackson Park is listed on the National Register of Historic Places.

The Obama Foundation estimates that the center will generate close to 5,000 direct and indirect jobs in surrounding Cook County during the construction and startup phase, and about 2,500 on a continuing basis. In response to neighborhood demands to share in the center’s potential economic benefits, officials have pledged to set aside 35% of construction jobs for residents of Chicago’s South and West sides and are also offering funding for job training.

Used to house records and boost legacies, libraries have been built for all past presidents since Herbert Hoover. Former President Donald Trump hasn’t yet publicly expressed much interest in a library. Doing so might imply he doesn’t plan to run for a third White House bid, something he has strongly suggested he might do.

Mr. Obama’s center will differ from those of his predecessors because it won’t technically be a library. Instead, the Obama Foundation will pay to digitize millions of pages of unclassified government records to make them available online.

The private foundation will run the complex rather than the National Archives and Records Administration, the federal agency that has traditionally operated the libraries and museums.

The intersection of Cornell Drive and Midway Plaisance is part of the redevelopment plan for the center.

The intersection of Cornell Drive and Midway Plaisance is part of the redevelopment plan for the center.

Almost $1 billion has already been raised for the project, with a current goal of about $1.6 billion to cover construction costs as well as an endowment for programming, Ms. Jarrett said.

The project is also putting significant dollars into the pockets of some Obama campaign and administration alumni and others who have landed jobs with the foundation. A tax document filed last year shows 16 people, including some former staff members, making six-figure salaries, ranging from $192,276 to $626,183.

While Mr. Obama remains popular in the heavily Democratic city, that status hasn’t translated into an easy glide path for his project. Challenges started after Mr. Obama announced that he would like to build in Jackson Park, a Chicago landmark designed shortly after the Civil War by Frederick Law Olmsted, one of two primary architects of Central Park in New York.

The most recent legal challenge was filed in April by a nonprofit called Protect Our Parks, as well as other plaintiffs. The federal lawsuit seeks to stop construction and alleges government agencies should have considered relocating the proposed center elsewhere to avoid traffic disruptions and environmental damage.

Bren Sheriff’s home is near Jackson Park. She said the center should be on private property instead.

Bren Sheriff’s home is near Jackson Park. She said the center should be on private property instead.

Bren Sheriff, one of the plaintiffs, said she isn’t opposed to the center being in Chicago. She just thinks it should be located on private property and not in a historic park near her home. “It will no longer be this pastoral scene,” the retiree and activist said.

Richard Epstein, a lawyer who represents Protect Our Parks, said he hopes his case is able to prevent the groundbreaking proposed by the Obama Foundation. “The Obamas would like to resolve this in three months,” he said. “It is not conceivable.”

Ms. Jarrett said the project is on a solid legal footing, especially following the successful completion earlier this year of all federal reviews. “The federal government ultimately gets to determine whether or not to give the green light, and they have given the green light,” she said.

While some in the surrounding neighborhoods are eager for the jobs the center might create, others worry that they’ll be driven out by rising rental prices.

“I’m very against it,” Bonnie Brendell, an 80-year-old woman who lives a few blocks from the center’s proposed location, said during a recent morning walk through Jackson Park. “There are so many other places where they could put it.”

Write to John McCormick at mccormick.john@wsj.com