Americans Are Desperate for Relief. The Rate Cut Is a Glimmer of Hope.

The Federal Reserve’s interest-rate cut on Wednesday will take time to work its way through the American economy. And not everyone will feel its effects right away. But for some, the move will amount to a big change—or at least the start of one—and those changes will add up.

The varied impacts will stretch from struggling restaurateurs north of Phoenix to Miami homeowners who need to downsize to get by. All told, the amount of extra breathing room in American budgets could shape the economy in the years ahead.

Officials on Wednesday cut their benchmark rate by 0.5 percentage point to start , the first step in lowering what Americans will pay for business and auto loans, as well as credit-card balances. Mortgage rates already have been falling for months in anticipation.

Now, the question is changing from how quickly higher rates will cool U.S. growth to how quickly lower rates can support it. The economy is more like an ocean liner than a speedboat: Just as it took time for higher rates to slow things down, it will take time for rate cuts to speed things up.

The cuts will make many household budgets stronger, on balance, and potentially begin to lift some of the bad economic vibes that have puzzled Washington and Wall Street. Across the world’s largest economy, those little differences are multiplied by millions of people who borrow money to finance big purchases, invest in companies or buy day-to-day necessities.

Take Alessandro and Clare Segala. The couple early this year made a bet that the typically slow-moving Fed would spring into action. After a monthslong search in Seattle’s red-hot housing market, the Segalas in January bought a three-bedroom townhome in the trendy Ballard neighborhood with a mortgage that carried a 6.99% rate. They gambled with higher monthly payments, figuring they would refinance once the Fed started cutting.

The catch: The timing was unclear. “We knew it was going to be painful for a little while,” said Alessandro Segala, a software engineer.

Even before the Fed’s cut Wednesday, the couple were already approached by their mortgage broker to refinance their loan. But they are waiting for enough cuts in the months ahead to shave about a point off their mortgage rate. The goal is to put $1,000 a month back in their pockets that they can invest elsewhere.

“That’s significant for us,” said Alessandro, 33 years old.

The Fed boosted its benchmark rate 11 times in 2022 and 2023, to between 5.25% and 5.5%. Wednesday’s cut puts it between 4.75% and 5%. Many economists think that level is still high enough to restrict growth—and it is much higher than the near-zero level of early 2022.

Still, sentiment matters. Now that rates are moving down, that alone could be enough to make more households and businesses feel all right about spending. The Fed’s projections released Wednesday suggested that the central bank will cut rates by another 1.5 percentage points by the end of next year.

“The things that we do really affect economic conditions for the most part with a lag,” Fed Chair Jerome Powell said at a news conference Wednesday. He added that the extent to which the cuts will affect borrowing costs such as mortgage rates will depend on how the economy performs.

Pointing to a promising slowdown in inflation but a recent uptick in unemployment, Powell said, “The U.S. economy is in a good place and our decision today is designed to keep it there.”

The rate cuts could have a quicker real-world impact because the U.S. is in much better shape than at the start of previous rate-cutting cycles. The economy is still adding jobs and Americans continue to shop, with August retail sales figures from the Commerce Department on Tuesday indicating consumer spending is growing solidly. The lift for the Fed this time should be a little bit easier.

Already, lenders have begun pre-emptively offering customers lower mortgage rates, with 30-year fixed rates falling to 6.09% this month from a 23-year high of 7.79% last fall, according to Freddie Mac.

The housing market, however, might feel the impact of the changes in fits and starts . In the past when rates dropped, homeowners often took it as an opportunity to refinance their mortgages and bolster their finances. A new wave of refinancing is less likely because so many homeowners already restructured their loans when rates were low.

The most recently available data from the Federal Housing Finance Agency shows that roughly one in seven residential mortgages had an interest rate of 6% or higher in the first quarter.

That still allows for some pickup in refinancing as rates go lower. Some homeowners also refinance not to take advantage of lower rates, but because they have an emergency need, such as an unexpected medical expense. Lower mortgage rates would somewhat lessen the blow of such crises.

In Florida, lower rates already have benefited homeowners such as Curtis Sponsler, 61, who has hit a rough patch in his work as a freelance animator. With rising costs for property insurance and groceries pressuring his finances, Sponsler and his wife, whose children recently left for college, have been looking to leave Miami and downsize to a smaller home.

“We just can’t afford it,” he said of his current house, which the couple bought with a 3.25% mortgage. “Every month we look at our spreadsheet and ask: ‘Where does all the money go?’ ”

Sponsler and his wife, Gaby Triana, who writes horror novels and other books , initially drew tepid interest on their property after listing it for sale this summer. “People were waiting for rates to drop,” he said.

In recent weeks, however, they entered a contract to sell for almost double the price they paid in 2017. The couple are using the profit to put 80% down on a less expensive house in Orlando. They plan to finance the rest through a mortgage with 5.5% interest—far lower than the market rate just months ago.

“We’re really lucky,” said Sponsler, who added that his monthly payment should fall by more than half. “But I do know so many people for whom the interest rates are killing them.”

That has also been true in the auto market, where the cost of car ownership has jumped in recent years alongside ballooning prices for used vehicles and insurance premiums. Buying a car isn’t a regular thing—few people get a new set of wheels every year—and because rates on most loans are fixed, drivers’ bills for cars they already own won’t change in the months ahead.

Even so, Fed cuts will gradually ease some of the pressure on prospective car buyers heading to dealerships such as Stehouwer Auto Sales in Grand Rapids, Mich. Three years ago, Vice President Kelly Herb said customers with top-tier credit scores could buy a year-old car with a loan that had an annual percentage rate as low as 2%. He estimated that the roughly 6% rates now common would translate to about $50 more a month under that scenario.

“When times are good, people don’t really ask about rates,” said Herb, whose customers struggle with more expensive child care and housing. “When times are like they are now, it’s one of the first things they ask.”

The used-car dealership now sells roughly 30 vehicles a month, the longtime salesman said, down from as many as 50 during the pandemic when rates were low and government stimulus was flowing. Despite cutting costs by reducing advertising and washing more cars in-house, Stehouwer is less profitable than it was then.

“Something has got to change,” Herb said. “I’m cautiously optimistic.”

More Americans have fallen behind on their car and credit-card bills this year, worrying economists, even as household debt relative to income is low by historical standards. While lower interest rates should provide relief, the impact on consumers who pull out the plastic at stores will be modest.

Cardholders carrying a $10,000 balance can expect each quarter-point Fed cut to shave just a few bucks off their monthly bill on average, said Brian Riley , co-head of payments at Javelin Strategy & Research. “You can be absolutely certain it’s not going to go down at the rate it went up,” he said.

That is cold comfort to Clarissa and Michel Cottabarren, who are fighting to save their 46-seat restaurant , Eurasia by Chef Michel. Many of their customers in Prescott, Ariz., are retired and on fixed incomes, and they aren’t spending like they did before inflation jumped.

In June, a truck crashed into the Eurasia building and forced the Cottabarrens to temporarily shut down. They paid for emergency repairs using personal credit cards. The eventual insurance payouts didn’t cover the full cost of the damage and lost business. The couple’s overlapping debts now include a roughly $60,000 credit-card balance.

“We just keep burying ourselves in a deeper, deeper hole,” Clarissa Cottabarren said. Keeping the restaurant open is costing them, but they can’t afford to close it, either. “We have given up our careers for this business,” she said. “We have no other source of income.”

The Cottabarrens have cut their employees’ hours, and they are washing more dishes and doing more late-night prep work themselves. Their hope is that an improving economy and a typically strong holiday season might make people a bit more likely to buy their noodle and rice dishes.

Both Catholic, the husband and wife returned to church recently for help coping with the toll of running a business on the edge of survival. “There’s no miracle yet,” Michel Cottabarren said. “But it is starting to get better.”

Write to David Uberti at david.uberti@wsj.com and Justin Lahart at Justin.Lahart@wsj.com