The maxim “good things come to those who wait” is being put to the test in the Presidio — where work formally begins Thursday on a 14-acre, sloping park intended to connect the atmospheric Main Post with ever-popular Crissy Field.

The target completion date was 2018 when a design team was selected in 2014 for what then was a $51 million project. Now the budget is $118 million — all but $20 million to come from private donors — and the space is set to open in fall 2021.

The reasons for the delay vary. What counts, says the project’s landscape architect, is that the result should show the time was put to good use. Instead of the gaunt viaduct that shadowed the area for generations, or the bare dirt that now covers two vehicle tunnels, there will be a naturalistic environment with coastal shrubs and panoramic views.

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“It’s been quite a process, but it has allowed the design to mature,” said James Corner, whose firm James Corner Field Operations is based in New York and best known for that city’s High Line. “It needed more richness of human experience, of topography, with a scale more comfortable for people.”

The essence of the design for what is called Tunnel Tops Park is the same as in 2015, when Field Operations won a competition held by the Presidio Trust, which manages nearly all of the 1,491-acre national park in the northwestern corner of San Francisco. There are gathering spaces inland, next to the Presidio’s visitor center, and a spacious child-friendly landscape along Mason Street facing Crissy Field and the bay.

In between: a re-created bluff that will slope down 35 feet, topped by a promenade and accented with three stone-clad outlooks.

But the form of the bluff is less voluptuous than before, the outlooks less dramatic. The “youth campus” adds two small buildings to the existing Crissy Field Center while sculpting the outdoor areas to let children feel lost in nature while they play or explore.

A “campfire circle” has been added near the visitor center — and beyond it, a hillock-like fourth overlook where a mundane Burger King once stood.

“This will be the first place where you encounter the (panoramic) view, the unveiling of the full horizon,” said Richard Kennedy, who runs Field Operations’ San Francisco office. “It’s another example of how we’re trying to amplify the experience of moving through the landscape.”

That desire is shared by the Presidio Trust, which is doing the project in collaboration with the National Park Service and the Golden Gate National Parks Conservancy.

“What they’re designing is a place where people will want to begin their Presidio experience,” said Michael Boland, who oversees the trust’s planning efforts. “It’s the main trailhead.”

Aspirations of this sort have framed the unusual project from the start.

The park is intended to complete the transformation of the descent from the Main Post and Crissy Field — evoking topography that was altered in the 1930s when the Doyle Drive viaduct was erected to link downtown San Francisco and the Golden Gate Bridge.

By the 1990s, it was clear that Doyle Drive needed to be replaced or given a full seismic makeover. Local landscape architect Michael Painter made the case that a ground-level roadway, tucked within tunnels part of the way, was the best way to heal a scar in a setting just beginning to make the transition from U.S. Army post to national park.

Since then, Crissy Field has been restored to become a regional attraction. Historic brick barracks along the parade ground have been restored. Tunnel Tops Park becomes the accessible vegetated link between the two — “the new Gateway to the Presidio,” read the competition brief issued in 2014, a site with “the potential to become one of the most iconic destinations in the country.”

Corner’s design team, which includes the local architecture firm EHDD, was selected nine months later. This being San Francisco, there were numerous public workshops while the initial design concept was massaged and refined.

And even though Presidio Parkway opened in 2015, there was a lengthy standoff between the trust and Caltrans over the details of how the state agency would return the construction site to the national park. That time was also spent raising money from affluent donors and foundations for a project where cost estimates continued to rise and the only public funding is $20 million from the Presidio Trust.

But all that is history. The emphasis now is a boisterous “groundmaking” Thursday, with speakers including Nancy Pelosi. There also will be the ceremonial start to the wider fundraising campaign, though $86.7 million already has been pledged by private donors.

For Corner, success will be best measured in a decade or so — after the plantings mature and the newness of the architecture fades.

“This isn’t about the tunnel tops being the showcase. We’ve always felt it should recede in some ways,” he said. “Over time it should get richer and richer, better and better, and then feel like it has always been there.”

John King is The San Francisco Chronicle’s urban design critic. Email: jking@sfchronicle.com Twitter: @johnkingsfchron