Beneath the art-bedecked terrazzo floor of San Francisco’s Salesforce Transit Center is an enormous concrete box waiting to be filled.

It’s an end point for bullet trains that may someday zip in from Los Angeles, and commuter Caltrain locomotives chugging up the Peninsula to the South of Market district.

But when the center opens Sunday, that concourse will remain empty. It will likely stay that way for years.

There is no firm timeline or funding source for the long-promised train service. While transportation officials seek to build momentum for this next phase, San Francisco City Hall is touting a new approach that could raise the cost to $6 billion from an already expensive $4 billion.

That’s caused some politicians and transit enthusiasts to worry, even as they remain adamant that the rail extension will happen. Because it must happen, said state Sen. Scott Wiener, D-San Francisco.

“Every major transformational transit project ever has been more expensive than we thought, had taken more time than we thought,” Wiener said. “We’ll find a way.”

For now, what’s about to open Sunday is little more than an immense bus station, served by Muni, AC Transit and other agencies. The underground rail service will be included as a second phase with the addition of bullet trains from Southern California and Caltrain commuter trains from the South Bay.

Most San Francisco officials and planners agree on the advantages of rail and its extension into downtown. South Bay commuters who are now dropped off at the edge of Mission Bay would step right onto Mission Street. Businesspeople would be whisked from Los Angeles to San Francisco in less than three hours. The concept of a transit hub shaped the dense high-rise neighborhood that’s risen around the Salesforce Transit Center, with its sleek sidewalks and cylindrical apartment towers.

Yet the mile-and-a half path from the transit center to Fourth and Townsend streets, Caltrain’s current terminus, is not virgin territory. It’s crisscrossed by busy streets and ramps to Interstate 280. Caltrain tracks that now are above ground cross 16th Street, a major entrance to the blossoming Mission Bay neighborhood.

The challenge of picking a route for the trains that would work for decades to come defies easy solutions. And it’s eluded City Hall and the Transbay Joint Powers Authority — the independent government agency in charge of the transit center and rail extension — for years.

“We’re building a 100-year system, at least,” said former San Francisco Planning Commission President Ron Miguel, who participated in a citizen working group to help conceive the new route. “So we have to think, ‘What do we want this to look like in 2070 — or beyond?’”

Under the authority’s current scenario, track would be laid underground from Seventh and Townsend streets to the transit center on Mission Street, leaving street-level rail crossings at 16th Street and Pennsylvania Avenue and at Seventh Street and Mission Bay Drive.

The city now wants to alter that idea because it would create huge snarls at the crossings, with longer electrified Caltrains and new bullet trains clogging the intersections for 25 minutes of every hour in neighborhoods that are rapidly growing.

“If you consider all the new housing and the new hospital coming into Mission Bay, that creates not only a traffic problem, but a safety problem,” said city Planning Director John Rahaim.

So, the Planning Department released a study in May recommending an alternate route that would start the tunnel at Pennsylvania Avenue and 25th Street, about a mile south of Seventh and Townsend, raising the project’s cost by $2 billion. City planners also called for tunnel-boring — mining deep beneath the street — instead of the cheaper construction method of tearing up roadway surfaces.

The proposed Pennsylvania Avenue extension quickly caught on at City Hall, finding favor with supervisors and other officials who have to agree on the route before the Joint Powers Authority can pursue it. After publishing the study in May, city planners presented it to neighborhood groups, the Planning Commission, the San Francisco County Transportation Authority and the Caltrain Board of Directors, among other bodies. In all cases it was “overwhelmingly well-received,” Rahaim said.

But the revision leaves out how to finance the project. So far the city has identified only $1 billion in funding from a mix of sources, including sales taxes and bridge toll money from Regional Measure 3 approved by voters in June. Much of the rest would come from federal and state funds that would need approval.

Serving the center As of Sunday, the following transit agencies will serve the center: AC Transit Golden Gate Transit Greyhound Muni Western Contra Costa Transit Authority Looking ahead Amtrak is in talks to run buses from its train stations in the East Bay, Sacramento and San Jose. Plans call for eventual use by Caltrain and a high-speed rail service from Southern California.

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Mark Zabaneh, the authority’s executive director, is resolutely optimistic.

He aims to have the rail line ready for construction by 2020, meaning all environmental reviews would need to be complete, and the right-of-way acquired to lay the original 1.3 miles of track from Seventh and Townsend streets to Second and Howard streets. He said the authority can start digging that route while it gets approvals for the Pennsylvania Avenue extension.

The money will follow, Zabaneh said, and if everything goes smoothly, the rail extension will be complete by 2029.

“I can tell you my glass is always half full,” he said. “When you look at all these megaprojects, funding is always the big challenge. You always have to believe that if you develop a funding plan and get your partners and the region behind it, then in due time, the funding will come.”

Still, skeptics and even some supporters worry about the escalating costs. Some note that the increase comes at an uncertain time for federal and state funding: The GOP-led federal government may be reluctant to shower funds on progressive San Francisco, Wiener said, and state officials are fighting to protect the newly enacted gas tax — a key source of revenue for the proposed rail line and other transit projects — from a ballot measure to repeal it this November.

“We probably have enough money to engineer everything, but do we have enough money to put a shovel in the ground? I don’t know,” said Greg Harper, who represents AC Transit on the Joint Powers Authority’s Board of Directors.

Further complicating matters, California’s high-speed rail system — which is already under construction — is beset by delays, ballooning costs and opposition from prominent Republicans, including President Trump. Its most powerful advocate, Gov. Jerry Brown, will leave office in January.

Supervisor Aaron Peskin, who chairs the board’s Transportation Authority, views the rail extension as a test of San Francisco’s ability to deliver major transit infrastructure. But it won’t work unless all the pieces come together, he said.

“If we don’t get Caltrain, and eventually high-speed rail, into Transbay Terminal it will go down as the most expensive bus terminal in the history of humankind,” he said.

Miguel, the former Planning Commission president, said the rail extension is too important to let that happen.

“This rail line, it’s as necessary to San Francisco’s transit vision for 2050 as BART was to regional transit” in the 1960s, he said.

Zabaneh said he looks forward to the day when trains will dash at blistering rates from Los Angeles Union Station, cutting a path through the Central Valley and into downtown San Francisco.

But during a recent presentation to the Transbay Joint Powers Authority board, he described the financing for the rail extension as “hand-to-mouth.”

He offered a wan smile. “And I expect we will continue that way,” he said.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com

Twitter: @rachelswan