Elon Musk has a history of making promises to rapidly deliver technological breakthroughs, only for them to end up taking longer than predicted or to fail to materialize.

Among these are his promises for fully autonomous self-driving cars or tunnels under Los Angeles to solve traffic congestion. Now some federal government officials worry that his pledges for landing astronauts on the moon will suffer similar delays.

That is why one of the largest federal contracts Mr. Musk has ever secured is now under intense scrutiny: a multibillion agreement with NASA for this crewed mission to the moon, the first in more than five decades.

The plan to invite private companies to develop a lunar lander for NASA was kicked off with much fanfare during President Trump’s first term, with a target of completing the mission by last year.

Other parts of the NASA moon mission are nearly ready, after their own delays and cost overruns, and are set to be subject to a full-scale flight around the moon with astronauts next year. But SpaceX’s lunar lander project is now so far behind schedule that there are increasing doubts the United States will beat China, which has its own plan with a targeted landing date of 2030, back to the moon.

The concerns, which have reached the White House, follow the falling out between Mr. Musk and President Trump, which led to a call by Mr. Trump and others inside the administration to at least initially look for SpaceX contracts to pare back or cancel.

But seven current and former senior NASA officials, in recent public statements and interviews with The New York Times, said their questions about SpaceX and its new Starship rocket had nothing to do with the public spat between the president and his biggest campaign donor.

Rather, they are nervous that Mr. Musk has once again overpromised on what he could achieve by now.

The 15-story-tall Starship has not yet carried any astronauts or commercial cargo. It has exploded during three of its four recent tests, sending a spectacular but potentially dangerous plume of debris over the Caribbean on two of those aborted trips to space. And its current version can carry only a fraction of its promised payload of at least 100 tons into low-Earth orbit.

Making matters worse, they say, Mr. Musk’s plan to carry two astronauts to the surface of the moon relies on a never-attempted refueling in space that the former NASA engineers say is so risky and behind schedule that it could be years before it is ready for the moon mission, meaning China is likely to get an astronaut there before the United States.

“This is not anything against SpaceX — they have done incredible things,” said Douglas Loverro, who served as the head of NASA’s human spaceflight division early in Mr. Trump’s first term. “But the further you move from known technology, the longer it takes to go ahead and get something done.”

Mr. Musk has missed a number of his own announced deadlines for the lunar project. For example, he predicted, and NASA announced, that SpaceX would attempt its first ship-to-ship fuel transfer test early this year, but that has now been delayed until at least 2026.

Mr. Musk, in remarks this month, expressed confidence that the Starship project continued to make progress.

“Unless we have some very major setbacks, SpaceX will demonstrate full reusability next year, catching both the booster and the ship, and being able to deliver over 100 tons to a useful orbit,” Mr. Musk said during a podcast, referring to three of SpaceX’s goals.

NASA is currently targeting 2027 for its mission, Artemis III. That will rely on a separate Space Launch System rocket, built by contractors other than SpaceX, to carry a spacecraft called Orion to get the astronauts to lunar orbit. The astronauts will then be transferred to SpaceX’s Starship for the moon landing — a sequence that is much more complicated than earlier NASA moon missions.

But privately, NASA officials are already acknowledging that the mission date is likely to slip to 2028. Mr. Loverro and other former NASA officials predicted that Starship, given its current challenges, would not be ready for its part of the moon mission until perhaps 2032.

Part of the problem, former NASA officials acknowledge, is they chose an excessively complicated lunar landing plan, starting during Mr. Trump’s first term. Trump administration officials back then did not take up a proposal to construct a lander based on existing, proven technology, said Mr. Loverro, who helped devise the alternative lander proposal starting in late 2019 when he joined NASA.

The White House liked the commercial approach. It shifted NASA toward the goal of buying space travel as a service, instead of the agency directly overseeing the work plan. That was less expensive and had a fixed price, avoiding the possibility of federal cost overruns, Mr. Loverro and a second former NASA official then involved in the deliberations said.

But the SpaceX plan meant far more risk.

“I was not firm enough in pushing what I should have pushed,” Mr. Loverro said in an interview this month.

Transportation Secretary Sean Duffy, the acting NASA administrator, said in a statement to The Times that he was standing by the current SpaceX plan.

The company, Mr. Duffy said in a recent interview with CBS News, has proved skeptics wrong before. In the process, it has built itself into the most important launch provider in world history. SpaceX’s workhorse Falcon 9 rocket has already carried nearly 120 successful missions to orbit this year.

“Secretary Duffy is focused on executing Artemis III under the current, long-planned architecture,” NASA said in a statement to The Times, adding that Mr. Duffy was “focused on ensuring we do everything we can at NASA to meet our targets and hold our commercial partners accountable to fulfill their contractually obligated deadlines.”

SpaceX did not respond to requests for comment.

Mr. Musk has acknowledged that SpaceX must clear considerable hurdles to get Starship fully operational, calling his effort “a candidate for most difficult engineering project ever.” But when discussing Starship, Mr. Musk is almost always focused on his eventual plans to take humans to Mars, not the moon mission, for which SpaceX has been paid about $3 billion.

“There are thousands of engineering challenges that remain for both the ship and the booster,” Mr. Musk said last month in a webcast from SpaceX’s offices before the most recent full-scale Starship test, its 10th such attempt, which was considered a success. Perfecting the heat shield on the Starship, so it can survive the fiery return to earth and quickly be reused, is one of the biggest challenges, he said.

NASA realized when it hired SpaceX that the company was taking on an enormous feat.

“SpaceX’s mission depends upon an operations approach of unprecedented pace, scale and synchronized movement of the vehicles in its architecture,” NASA said in its official selection statement in 2021, when it formally picked Starship.

The lander mission is supposed to place two astronauts at the south pole of the moon, where they would remain for about a week before being carried again by Starship to lunar orbit, then return to Earth in the Orion capsule.

All of the stages of the Artemis III project have encountered delays. The Orion and Space Launch System, built by a group of contractors including L3Harris Technologies, Boeing and Lockheed Martin, are also billions of dollars over budget.

But the Starship piece is considered by most former NASA officials to be the riskiest, and most likely to face significant additional delays. That is because it is responsible for the largest number of unproven technological advances necessary to complete the mission, according to a NASA report last year.

These include a reusable Starship two-stage rocket system, the largest ever built. It also requires Starship launchpads and other ground operations that can handle 15 or more rapid-in-succession launches needed to refill the Starship tanks once they get to orbit, which creates considerable risk for an accident.

Landing such a tall rocket — Starship moon lander will be about 165 feet, compared with the Apollo Lunar lander that was 23 feet tall — means it can carry much more cargo, but it creates greater risk that Starship could topple once it arrives on the moon, Mr. Loverro said.

After it has all the pieces built, SpaceX still needs to fly at least one uncrewed mission to the lunar surface to prove it can work, adding more time.

“This is all important technology that I agree we’re going to need when we go to Mars, for sure,” said Douglas Cooke, who spent nearly four decades at NASA before retiring in 2011, and has recently served on a NASA independent review team and as a consultant to Boeing. “But it’s in the path of trying to get back to the moon quick.”

Mr. Loverro, Mr. Cooke and a third former senior NASA official, Daniel Dumbacher, in an opinion piece in SpaceNews this month, argued that NASA needed to devise a new plan to get quickly to the moon. “If a ‘Plan B’ is needed, that planning needs to start now,” they said, or the United States will lose the race back to the moon.

This could include reviving the earlier plan for a simple, proven lunar lander design that could be built in about five years and not require orbital refueling, the former NASA officials said.

Without such a shift, the United States is likely to lose the race, the former NASA officials predicted.

“I doubt that’s going to be accomplished by 2030,” Mr. Dumbacher said of the SpaceX moon landing plan in an interview, “and that makes it likely that China will beat us to the moon.”

Mr. Duffy reacted angrily to these recent predictions that the United States was behind China, in part because of Starship delays.

“We are going to beat the Chinese to the moon,” Mr. Duffy said, according to a recording of a virtual town hall meeting with NASA employees this month. “We are going to make sure that we do this safely. We’re going to do it fast. We’re going to do it right.”

William Gerstenmaier, an aerospace engineer and a former NASA senior administrator who is now a top SpaceX executive, said in a speech this month that by next year an uncrewed Starship would have made a full orbit of the earth, for the first time.

Again his focus was on Mars, another planned mission where Mr. Musk has made bold predictions for how quickly he might get there.

“Ultimately, SpaceX is about really Mars,” Mr. Gerstenmaier said. “And that’s what we’re trying to do.”

Kenneth Chang contributed reporting.