Authorities have said extracting the entire team from the cave could take up to four days, but Sunday's success raised hopes that it could be done faster.
A source involved in the rescue mission who saw two of the four boys walk out of the cave told Reuters that they looked exhausted but healthy, adding that one even looked "vivacious and fresh".
It is understood the same divers who rescued the first four boys have been given the job of getting the remaining team members out.
Less than an hour earlier, an ambulance with flashing lights had left the cave complex, hours after the start of the second phase of an operation to rescue the soccer team. The rescued children were taken to the hospital, and officials said early Monday that they are strong and safe but need to undergo detailed medical checks.
Musk and his team hope the skinny sub will aid in the rescue of the remaining five members of the youth soccer team who are trapped in a cave, but if the rescuers succeed on their own, Musk sees the sub as a future tool in high-risk rescues.
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The four boys guided from the cave Sunday in an urgent and risky operation that involved them diving through the cave's dark, tight and twisting passages were happy and in good health, authorities said. However, they got trapped inside after heavy rains flooded the entrance of the cave.
Narongsak said the rescued boys had not been identified out of respect for the families whose sons were still trapped, adding that the boys were being kept away from their parents due to fear of infection.
CNN reported that the rescue operation had resumed.
The boys, aged between 11 and 16, went missing with their 25-year-old coach after soccer practice on June 23, setting out on an adventure to explore the cave complex near the border with Myanmar and celebrate a boy's birthday.
A deluge could overwhelm efforts to lower water levels in the caves - more than 32 million gallons of water were pumped out after the boys were found alive last Monday. As of Sunday evening local time, four boys had been successfully removed from the cave.
In an indication of how unsafe the journey can be, a former Thai navy diver died in the caves on Friday. Following torrential rainfall, the cave was quickly flooded and the group had to move several kilometers inward to find dry land. Rescuers have been racing against the clock to beat the next downpour, which could make the operation much more hard.
The soccer team had been trapped in the underground cave network since June 23, with flash floods causing water levels to rise, making it hard to get out.