Faced with a sudden ridership explosion on Amtrak trains, the Carter administration is beginning to have second thoughts about its proposal to eliminate 43 percent of the nation's rail passenger service next fall.

Administration sources confirmed yesterday White House domestic policy officials, working with the Department of Transportation, have begun a review of the Amtrak proposal. Officials said letters from senators and congressmen have been piling up in the office of Transportation Secretary Brock Adams urging a review of the cuts.

"Our business is topping out . . . because we're out of equipment," with no potential for increasing the number of passenger cars Amtrak has in less than about three years' time, Boyd said in an interview.

Gasoline shortages and fears about the ability of some people to travel this summer by automobile, combined with the long United Air Lines strike and the crush caused by the grounding of the DC10 airliners, have brought more customers to Amtrak than at any time since it was formed by Congress in 1971.

During May, Amtrak reported yesterday, the dollar volume of ticket sales soared 72 1/2 percent to $33 million compared with $19 million in the same month last year. Advance reservations are running 90 percent ahead of the 1978 levels and some trains now are carrying standing passengers.

The rediscovery of the railroads came as Congress was confronted with the administration's Amtrak cutback proposals, first announced in January.

But Amtrak President Alan Boyd warned yesterday that even if there is a policy change, there is no way the rail system can build up a fleet of passenger cars fast enough to handle sudden travel demands.

Since neither house acted last month to veto the Carter plan, Amtrak is required to eliminate services over 43 percent of its 27,000-mile system as of Oct. 1. Two-dozen long-distance trains would be stopped and rail service to such cities as Atlanta, Indianapolis and Dalls-Fort Worth would be ended.

Later this month, DOT and Amtrak officials will sit down to review a new survey of passenger ridership being developed by the government-subsidized railroad, which could lead to some changes in the administration plan.

"If Amtrak comes up with the figures. . . . we don't want to be locked in" to cutting out trains with new-found riders, that may make them potentially viable in the long run," DOT spokesman Jerry Klingerman said yesterday.

At the same time, Klingerman emphasized that DOT "remains happy" with the 43 percent cutback now contemplated and he noted that many of the trains now being crowded - such as the Los Angeles-San Diego route - are among those that would be continued in any event.

"We aren't doing this [cutback] with a vision of penalizing anybody," Klingerman added, pointing to DOT statistics showing that 91 percent of current riders still would receive rail service under the proposed cutback. The cutbacks are designed to reduce the federal subsidy to Amtrak by $1.4 billion over the next five years.

The DOT spokesman and Amtrak's Boyd also agreed that the biggest question about the new boom in rail passenger business is: How long will it last? "There is an energy crisis and we expect to sport shortages (of gasoline) . . . but as people get more used to it, who knows whether this Amtrak increase will be there," said Kingerman.

Boyd said a true picture of the permanent ridership gain won't be available until September figures are gathered - the first month after a normal increase experienced every summer. Only at that time can Amtrak consider placing orders for new passenger cars, he added. There was a similar - but smaller - gain in Amtrak business after the Arab oil embargo in 1974 although most riders returned to their cars thereafter.

But the Amtrak chief executive said he expects a different reaction this time. "Trains are in fact capable of being energy-efficient on a relative basis," Boyd said. "As the reality of the energy shortage permeates the consciousness of more people, there's going to be greater and greater demand for alternative forms of transportation, which will be proved by the railroad."

Boyd also emphasized yesterday that he does favor some cutback in Amtrak's routes, because he doesn't have available equipment to operate current routes efficiently and at proper levels of service. Amtrak begins the summer of 1979 with record demand but 100 fewer passenger cars than a year ago - all of which had been owned by private railroads and were built decades ago.

"We're trying to mend and make do," said Boyd, who has ordered renovations for 84 cars that were "in the boneyard" and put a hold on plans to send 300 old cars to the scrap heap. Amtrak officials also have been asked by Boyd to contact the one remaining U.S. passenger car manufacturer - Budd Co. - about when new Amtrak cars could be placed into production. Separate contacts are being made with the railroads of Mexico and Canada, and West European manufacturers, about the availability of any cars.

Amtrak ordered 284 new bilevel cars for service in the Western states from Pullman Inc. in 1975 but because of strikes, only 23 are in service today. And Pullman has announced plans to retire from the rail passenger car manufacturing business when the current production run is completed.

Meanwhile, Boyd is operating perhaps the only billion-dollar corporation in America that has no idea about what services it can offer after Oct. 1. Boyd must make decisions on such things as whether to accept reservations after that date for trains due to be dropped, whether to order tickets and timetables and whether to order food stocks for dining and snack cars.

The Senate is scheduled to take up Amtrak legislation later this month but the House is not expected to act until July, at the earliest. Boyd conceded that he may not know the fate of Amtrak until late in the summer, since many congressmen have amendments planned that would exempt certain trains from the proposed cutback. CAPTION: Picture, Amtrak President Alan Boyd at interview in his office, overlooking the Capitol. By Frank Johnston - The Washington Post