The children will need to be led through the Tham Luang cave, which consists of a series of narrow, waterlogged passageways, for around two-and-a-half miles in poor visibility.
Even the most experienced divers find the route challenging, and a former Thai Navy Seal died on Friday trying to make the journey.
The rescue has become even more urgent following news heavy rains are expected to return to the region, which could shrink the air pocket where the team has been trapped to less than 10 square metres.
Tossathep Boonthong, chief of Chiang Rai's health department and part of the rescue team, has confirmed to journalists that two boys have been rescued from the cave.
“Two kids are out. They are currently at the field hospital near the cave,” he said.
“We are giving them a physical examination. They have not been moved to Chiang Rai hospital yet.”
A medical team for each of the 12 boys and their coach are on standby outside the cave.
After an initial assessment at the site, the boys will be airlifted to a makeshift helipad close to the Chiang Rai Prachanukroh hospital, around 40 miles (70 km) away.
A source at the hospital said that five emergency response doctors were awaiting the party and a further 30 doctors were on stand-by, adding that everyone was feeling tense.
“The teams here are happy the boys are being rescued but also anxious about the severity of the boys' conditions. We're under a lot of pressure,” she said, declining to be named because she was not allowed to speak to the media.
Elon Musk has offered to assist the rescue efforts
A team of drilling and exploration experts from entrepreneur Elon Musk’s SpaceX and Boring Company firms is expected to reach the cave site on Sunday, Thailand's defence ministry said.
Mr Musk has previously said one of his companies is aiming to develop a “kid-size” submarine to assist with the rescue.
“Got more great feedback from Thailand,” he tweeted.
“Primary path is basically a tiny, kid-size submarine ... Light enough to be carried by 2 divers, small enough to get through narrow gaps. Extremely robust,” he added, revealing it would take eight hours to build and 17 hours to send to Thailand.
The boys will be led through an extremely challenging series of passageways sometimes no more than two feet (60cm) wide that have proved so difficult to navigate even for some of the world’s leading divers.
The Thai government has released a graphic demonstrating how divers hope the rescue mission will unfold.
Each boy will be guided through the cave complex by two divers, guided by a rope. At the narrowest points, divers will detach their oxygen tanks and slowly push them through the gap.
The Thai Navy Seals, who have been spearheading the rescue effort, have posted a photo on their Facebook page with a vow to bring the boys from the trapped Wild Boars football team home.
“We, the Thai team and the international team, will bring the Wild Boars home,” the unit said in the message.
With expert divers needing around 11 hours to complete a round trip through the hazardous cave network, it may be around 9pm local time (3pm BST) before the first children emerge if the mission proves successful.
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