It has been suggested that they may need to learn how to scuba dive in order to escape, but none of the children can swim and cave diving is a notoriously risky sport, as emphasised by the death of one of their rescuers, Saman Gunan, a former navy diver, in the caves on Friday.
The Thai defence ministry said a team from a Musk firm with drilling and exploration knowhow should reach the cave on Sunday.
Cave rescue experts have said it could be safest to simply supply the boys where they are, and wait for the flooding to subside. "And please tell the coach we don't blame him and don't feel any guilty".
The death of an experienced rescue diver in the cave system underlined the inherent risks in attempting to move the boys.
"Teacher, don't give us lots of homework!" read one. Crews are working to install a three-mile long oxygen tube and have delivered additional tanks to the boys. "They'll be looking at flow rates, recorded rain fall over the past weeks, months to get a rough indicator of where they're at, they'll have a deadline in mind, and then they'll go for the most unpopular way out", he added. But authorities said it remained unclear how long the boys would have to remain inside.
The boys were exploring the cave on 23 June when they were cut off by water. The rescue team also includes divers and workers from Australia, the United Kingdom, and other parts of Europe and Asia. Getting trained divers in is easier than getting untrained kids out. Earlier efforts to pump out water from the cave have been set back every time there has been a heavy downpour.
"I confirm that we are at war with water and time from the first day up to today", he said. He also thanked worldwide experts who helped find the boys.
Family and friends expressed relief when the boys were found, but video of the gaunt, disheveled lost youngsters released this week has only partially reassured their loved ones. "He's thinner", she said, as she ran her finger over the image of her son on a television screen. But attention turns to the hard task of getting the boys out safely.
Some started to suggest the reason the boys had yet to be found was due to holy spirits residing in the cave.
To date, Thai authorities have drilled more than 100 holes in the mountain. "There is limited time", Narongsak Osottanakorn, head of the rescue mission and Chiang Rai's former governor, told a midnight media briefing.
Thailand's Navy SEAL commander also said rescuers may have little choice but to attempt the hard extraction of the group.
A former Thai navy SEAL diver, Samarn Kunan, died from a lack of oxygen on Friday as he navigated the cave complex close to the Myanmar border.
Rescue teams have been pumping millions of liters of water from the cave in an attempt drain the cave but the impending weekend rains threaten to undermine the work.
"Despite this, we will continue until we accomplish our mission", Arpakorn said Friday.
Written by hand on water-stained graph paper, letters from the 12 boys, coach and divers caring for them were published Saturday morning by the official Facebook page of the Thai Navy SEAL.
But more rain could erase that progress.The group's 25-year-old soccer coach, trapped with his 12 players aged 11 to 16, has written an apology to the children's parents, which was ferried out by expert divers attending to the group trapped in the cave.
"The SEAL team takes very good care of us", wrote Panumat "Mix" Saengdee, 14.
One boy wrote: "Don't worry that I am missing for two weeks, I will help you at the shop soon".
The coach's role in the team's predicament has split Thai social media.