They come from Brazil, Burkina Faso, Uzbekistan, India and dozens of other countries, a moving global village of hundreds of thousands of people crossing the Rio Grande and slipping through gaps in the border wall at a pace of nearly 9,000 people a day, one of the highest rates of unlawful crossings in months.

Despite new border barriers and thickets of razor wire, risk of deportation and pleas for patience, a resurgent tide of men, women and children is not waiting. Driven by desperation, families and individuals are pushing across the southern border and past new efforts by the Biden administration to keep migrants waiting until they secure hard-to-get appointments to enter the nation with permission.

The influx is creating a humanitarian and political crisis that stretches from packed migrant processing facilities in border states to major American cities struggling to house and educate the new families. Though many get through, thousands are being sent back across the border or on flights to their home countries. But from Texas to California, more than two dozen migrants who have entered illegally in recent days said they could not afford to wait.

“If you don’t take risks, you cannot win,” said Daniel Soto, 35, who crossed with his mother on Tuesday after they sold their car, restaurant and house in Lima, Peru, betting their entire fortune of $25,000 on a weeklong journey to the border near Tijuana.

Surges in migration at the southern border, while motivated by poverty, violence and hunger, are also tied to weather patterns, policy changes and personal circumstances. The pace of unlawful crossings dropped sharply in the spring amid uncertainty surrounding the end of a pandemic-era measure that allowed the government to quickly deport migrants. But numbers rebounded over the summer, and are now nearly double the 4,900 unlawful crossings a day that were recorded in mid-April.

The Biden administration also allowed nearly 500,000 Venezuelan migrants who are already in the country to seek work permits and protection from deportation. The administration yielded to pressure from leaders in New York, where the recent arrival of more than 100,000 migrants in New York City has overwhelmed shelters and strained resources. Though the Biden program doesn’t apply to new arrivals, it touched off debate about whether the action would encourage more people to migrate.

Yet those moves are not enough to meet the tremendous demand, and they cannot compete with the misinformation spread by smuggling networks — a multimillion-dollar industry — or the messages sent home from other migrants who made it into the United States.

Migrants like Mr. Soto and his mother are arriving on a tailwind of stories of friends and relatives who reached New York or Chicago months earlier. Many also believe false claims from smugglers and social media that migrants would definitely be able to remain in the United States if they could make it in.

“The smuggling organizations are spreading misinformation with a global reach that they couldn’t do before,” said John Modlin, the Border Patrol’s Tucson sector chief, who is coordinating the response to border crossings in Arizona and California. “In the past, at best, they could talk to the village they were in, or a small region. Through social media, they can hit people all around the world.”

Mr. Modlin said border agents are “recovering bodies almost every day of people not making it.”

Thousands of migrants who do cross the border successfully are being deported shortly after they arrive, based on factors that include their home countries, available flights, and the discretion of border officials. But others file asylum claims when they face deportation in immigration court, and are allowed to remain in the United States while they wait for their cases to wind through immigration court, a process that can take years.

Some people will not show up for their court proceedings, and continue to live and work in the United States along with millions of other undocumented immigrants.

Some migrants who arrive using the government app are eligible for permission to stay in the country and work for two years, but may still eventually be ordered deported.

“It will work out,” said Diego Santos, a 23-year-old Brazilian who was heading to Philadelphia after being released by border authorities in San Diego. Ahead of him lay the hope of construction work, but also deportation proceedings that he now has to fight.

“I’ll do what I can to stay,” he said.

As new arrivals swamp processing facilities and strain the capacity of shelters, the Border Patrol has begun dropping off many migrants outside churches, supermarkets and gas stations, transforming border cities into scenes of confusion and triage.

In San Diego, the Border Patrol released thousands of people in the last week near a hub for trolleys and buses, many of them with little money or idea where they were.

Mamadou Barry, 19, who had traveled from Guinea, carried paperwork from U.S. authorities saying he had “failed to provide address” of his final destination. Officials had scheduled his first deportation court hearing in Los Angeles. But he knew no one there, or anywhere.

In the border city of Nogales, Ariz., local officials and nonprofit groups have scrambled to arrange for buses to take newly released migrants to a shelter in Tucson, an hour’s drive north. But one evening this week, immigration vans released 30 people in Nogales three hours after the day’s last bus to Tucson had left.

“Where are we going to sleep?” asked Liliana Quishpe, 44, who had arrived from Guatemala with her 17-year-old daughter. “They just left us here.”

The surge shows little sign of ebbing, according to Brandon Judd, the head of the Border Patrol union, who said that 8,900 people were arrested on Wednesday and another 8,360 on Thursday.

In interviews, many newly arrived migrants said they made plans to travel to the United States as soon as they had cobbled together the money to pay for the trip. Most did not plan to stay at the border, and with the aid of a network of nonprofit groups on the U.S. side, quickly set off for other cities where jobs, relatives or the promise of space in a shelter awaited them.

In Texas, Yosnavys Venta, a 23-year-old from Venezuela, said he spent six months in Mexico trying again and again to get an appointment using the new mobile app. Some who have used the app said they were able to secure appointments right away, others said they could not get one for months.

Mr. Venta finally gave up earlier this month and decided to take his chances in joining thousands of migrants who sloshed across the Rio Grande and into the overwhelmed city of Eagle Pass, Texas.

So many migrants have poured in to the city that on Thursday, the mayor authorized law enforcement officers to arrest people for trespassing if they clamber onto the banks of a city-owned riverside park. Mayor Rolando Salinas, a Democrat, said his small city can’t sustain thousands of migrants coming into the community.

Gov. Katie Hobbs of Arizona, a Democrat, joined border law-enforcement officials and mayors in criticizing the Biden administration for what she called haphazard releases of migrants. “Arizona is being overwhelmed,” she said Friday.

Even places with more resources, like Pima County, Ariz., are struggling.

“It’s been really hectic,” said Mark Evans, a spokesman for Pima County, which runs buses that collect migrants from small border towns and take them to a large shelter in Tucson. “We shouldn’t be doing this. There’s an entire federal agency designed to provide this kind of shelter, and that’s FEMA.”

Blas Nuñez-Neto, an assistant secretary of Homeland Security, said the influx of migrants from countries beyond Mexico and Central America had put “an incredible amount of pressure” on the system.

The Biden administration has expanded the number of appointments available to migrants who use the mobile app, scheduling some 43,000 appointments a month.

Demand still far outstrips available slots, though, and many migrant families who are stranded in fetid, dangerous makeshift tent encampments along the Mexican side of the border have given up trying to use the app, preferring to brave a perilous crossing across the Rio Grande and often paying cartels that control the river.

“They are tired of waiting,” said Juan Fierro Garcia, a pastor in the El Buen Samaritano migrant shelter, in Juarez, Mexico. “They are more desperate.”

In Arizona, Walter Garcia, a 26-year-old firefighter from Guatemala, is among many migrants who barely even considered the legal route. Like many people making their way to the U.S., he had never heard of the new app.

His mother had managed to slip into the United States through the desert a year ago, so Mr. Garcia figured that he could do the same. He paid a smuggler $3,000 last week to take him to a gash in the border wall in Arizona, and on Wednesday, Mr. Garcia was freed from immigration custody and waiting at the Tucson airport for a flight to New Jersey to meet his mother.

“Two days in immigration, and we’re out,” he said. “It was easy.”

Migrant shelters in Texas, Arizona and California say they are struggling to find cots and hotel rooms to house the hundreds of new families and single adults who arrive every day, and local governments have scrambled to keep up with the pace of migrants being released onto the streets.

Outside a community center in San Diego, Ender Pirela, a 23-year-old from Venezuela, recalled how he had almost given up waiting for an appointment to enter the United States.

Mr. Pirela’s older brother had used the new app to enter six months ago, and ended up in Dallas. He worked at construction and saved $2,500 so that Ender could make the same journey.

Mr. Pirela said he and two traveling companions spent six weeks in Monterey, Mexico, where they were harassed and robbed and forced to sleep on the street when they ran out of money. Many other migrants, fearing for their safety, gave up waiting and crossed illegally, he said, but he waited.

“When our date arrived,” Mr. Pirela said, “there were tears everywhere.”

Reporting was contributed by Julie Turkewitz, Edgar Sandoval, J. David Goodman, Reyes Mata III and Rob D’Amico.