Froylán Martínez's bare feet pounded the concrete court without a sound as he steamed past his opponents, but the spectacular show of speed ended with a disappointing shot at the hoop high above his head. Undeterred, the diminutive 10-year-old – a rising star of Mexican indigenous basketball spun to pursue the ball, and keep chasing his dream.

"I want to play in the NBA," Froylán said after the game, which launched trials for an internationally successful team drawn from the isolated Triqui indigenous people in southern Mexico. "I'm fast but I need to work on my shots."

When a former professional basketball player set out to find fresh talent here four years ago, the Triqui region was primarily known for its inter-clan feuds, political violence and underage brides. Now the Mexican Academy of Indigenous Basketball, and its remarkable team, have become a symbol of hope forged in adversity.

"This is about noticing the talent of indigenous people who have been forgotten by their own country," said Sergio Zúñiga, who now hopes to replicate the experiment in indigenous communities across the country. "If we could build all this out of nothing, the future of Mexico can change too."

Zúñiga first presented his plan to the leaders of the fiercely independent Triqui people, one of Mexico's smaller indigenous groups with a population of around 24,000, concentrated in Oaxaca state. In this harsh region, basketball has long been the only sport practiced with any regularity, because there is not enough flat land to play football.

But Zúñiga's proposal was initially met with suspicion. It didn't help that the coach made his pitch a week after two human rights activists were killed while investigating the earlier deaths of two community radio announcers.

"They thought I was a spy, they thought I wanted to steal the kids and sell them," Zúñiga said. "It was very complicated at first, but little by little the impact became clear."

With a seriousness and persistence rarely seen in Mexican sporting projects, Zúñiga slowly put together the team. Initially they played without shoes, because their parents could not afford them. But what they lacked in footwear and stature, they made up for in speed, resilience and determination, and soon their performances in Mexican tournaments were grabbing the attention of the basketball cognoscente.

This brought in a trickle of donations, which last year allowed Zúñiga to move the 25-member A-team seven hours drive away to a communal house just outside the state capital, so they train after school and at the weekend.

Then, in October, the team won a tournament in Argentina – just after Mexico's footballing elite had become a national embarrassment as it struggled to secure a place in the World Cup.

Largely unknown before they left the country, the Triquis returned home to find they had been catapulted into celebrity. Now they play on a shiny new court built with money from the office of President Enrique Peña Nieto, who jumped at the chance of association with an inspirational good news story far from the drug war violence that tends to dominate news from Mexico.

However, despite its focus on sport the project offers an implicit criticism of Mexico's abandonment of its indigenous population: according to the latest official figures (from 2012), around 80% of indigenous Mexicans live in poverty, compared to a national figure of 46%, and 27% are illiterate– a proportion five times greater than for the general population.

In this part of the state of Oaxaca most families live in one room adobe houses, signs of malnutrition are obvious, and mobile phone reception is a rarity,

Children who join the Triqui team are offered educational opportunities they would otherwise never have, and are encouraged to contribute to the development of their communities if they make it through university. "The basketball is the bait," Zúñiga said.

Team members must keep up their grades, speak Triqui at home, and follow strict discipline that includes penalties of 300 push-ups for displays of aggression on or off the court.

Meanwhile, the stories they tell of visits to Disney World and travelling on planes can seem even more effective propaganda for the project than the trophies they have brought home to a region with an established tradition of migration to the US.

"Maybe one day my son will go to the United States with a passport," mused Alejandro de Jesus, who has made the dangerous journey across the border several times, guided by people smugglers. His nine-year old son now plays for the team. "I want him to have a different life from me."

Local coaches trained by Zúñiga are also pushing to increase their recruitment of girls who, among the Triqui, are regularly forced into marriage, motherhood and domestic servitude from the age of 13.

At the Olympic-style parade of local communities before the recent trials, a group of girls marched behind the banner of El Rastrojo. Aged between 10 and 13, the girls said their mothers had reluctantly given their blessing – along with warnings that too much physical exertion would leave them barren. The warnings only fuelled their enthusiasm.

"We don't want children, they get in the way and you have to look after them," Esperanza said to the general agreement from her friends. As she waited to show off her skills on the mountain-edge court that doubles up as the primary school playground, the 10-year-old said: "I want to travel too. I want to see other places."

After three days of trials, 100 children were selected; later they will be whittled down to 25 reinforcements for the A-team in the city. Now the team is nationally known, the pressure is on to maintain their winning streak.

Meanwhile, a handful of existing members are already being groomed for scholarships abroad. These include Quirino Merino, who played the exhibition game in El Rastrojo in trainers – a sign that the process of "profesionalisation" has already begun.

"I like playing without shoes better," the 10-year-old said. "Shoes feel heavy, they slow you down and they give you blisters, but I'm getting used to them now."

• This article was amended on 28 April 2014. It originally stated that most adult women still wear the traditional long, red embroidered smocks in a particular part of Oaxaco. The statement, while correct, implied this was a negative thing in the context of the paragraph. This was not the intention and it has been removed for clarity.