They came amid the ice and snow, bundled in parkas and long johns, expecting an hourslong wait in the subfreezing temperatures and whipping winds.

Instead, the mourners who journeyed through the maze of barricades around the Capitol to pay their final respects to President Jimmy Carter were shocked to find such a short queue, waiting just 10 to 20 minutes at most to honor the 39th president, who died at 100 last month.

Parents pushed strollers. Children and adults alike lumbered into the Capitol dressed in insulated snow pants and clunky winter boots. No celebrities, sports stars or internet icons made appearances in the Rotunda, as they have for previous presidents.

But President-elect Donald J. Trump and his wife, Melania, were expected to pay their respects later Wednesday.

And the slow and steady stream of regular people — as well as several members of Congress, staff, military leaders and dignitaries — seemed a fitting tableau for the lying-in-state of the humble peanut farmer from Georgia, who prided himself on living more than 60 years in a four-bedroom home valued at just over $250,000.

First in line to bid farewell to Mr. Carter was Chris Forward, a Virginia educator who showed up on Tuesday afternoon, just before Vice President Kamala Harris and congressional leaders gathered to eulogize Mr. Carter in a closed-door ceremony in the Rotunda.

“I was sort of surprised,” said Ms. Forward, who became fast friends with three other women who joined the line shortly after she did. “I thought it’d be a long wait because he was such a great man.”

Peter and Uta Schreiner, a couple from Germany, were also near the front of the line. During a trip to the United States to celebrate Mr. Schreiner’s 50th birthday, they had been attending a Washington Commanders football game on Dec. 29 when they learned that Mr. Carter had died. Then winter weather delayed their flight back home until Thursday, and the couple decided to head to the Capitol to pay their respects.

“It’s a special moment. It’s hard to describe — it’s incredible to be a part of all this,” Mr. Schreiner said. “He was a special man, and it’s an honor to be here right now to give him the last honor.”

As well-wishers slowly processed around the coffin, some wiping tears and others somberly bowing their heads, a near silence gripped the cavernous and echoey hall under the Capitol dome, which is usually awash with noise from tourists and frenzied staffers. Only the shutters of cameras, yelps from agitated children and the occasional cough or stray cellphone alert broke the hush.

The solemn ritual in the Capitol was a prelude to Mr. Carter’s state funeral on Thursday morning at Washington National Cathedral, which the four living presidents will attend and where President Biden is scheduled to deliver a eulogy.

Throughout the day on Wednesday, several members of Congress passed through the Rotunda to pay tribute, including Senator Mitch McConnell of Kentucky, the former Republican leader, and Senator Tammy Duckworth of Illinois, a Democrat and one of the Senate’s first female combat veterans, who offered a salute.

Becky Carter, the president’s daughter-in-law, arrived on Wednesday afternoon to shake hands with mourners and thank them for coming.

“God bless you,” one of them told her.

Carlos Del Toro, the secretary of the Navy, stood in silence as he honored Mr. Carter, a Naval Academy graduate and veteran submariner, before laying a hand on his flag-draped coffin. Thomas Donilon, who worked for Mr. Carter and served as President Barack Obama’s national security adviser, also stopped by to pay his respects.

Most who came to the Capitol to mourn Mr. Carter were not old enough to remember his presidency. But many lauded his legacy as a humanitarian and pointed to him as an example of decency and humility in a world racked with incivility.

Shermanda Williams of Maryland, who came with her two sons, said she had brought them to teach them about “having the heart for humanity,” as the former president did.

“That was very, very important to come and show our respect,” Ms. Williams said, “and to let them see that someone who is kind and gentle and concerned about others can be successful.”

Her younger son, 11-year-old Kellen, chose to come to the Capitol even though he could have enjoyed a free day at home since school was canceled because of the winter weather.

“Jimmy Carter was a great man,” he said. “With all his decisions, he was not going to make everybody happy, but he made as many people happy as he could. Because nobody — no country — is perfect, so he did all he could.”