Chiang Rai governor Narongsak Osattanakorn described the four rescued boys as in "perfect" health, despite earlier reports that one was being "closely monitored", calling the rescue "our masterpiece work".
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.
And, in fact, at this morning's press conference that announced the beginning of the operation, a Thai general said he thought the operation could take two or three or even four days depending on the circumstances. But authorities have said it remains unclear how long the boys would have to remain inside.
"The prime minister said that this kind of event should never happen again on Thai soil", Narongsak told reporters.
Experienced cave rescue experts consider an underwater escape a last resort, especially as the boys are untrained in diving.
Former Chiang Rai Governor and Rescue Chief Narongsak Ossotnakorn has confirmed to reporters the first four boys have been safely rescued from the waterlogged caves and are now in hospital. All four of those rescued yesterday were safe, he said.
"The operation today went quicker than when we rehearsed, 10 minutes quicker", he said, according to CNN.
An additional eight boys, ages 11 to 16, and their 25-year-old coach are still inside the Tham Luang cave, where they've been trapped by flood waters since June 23.
It is expected that the operation will continue in the next 12 hours.
It was not clear who was inside the ambulance or the helicopter.
Sunday's mission involved 13 foreign divers and five Thai navy SEALs.
The rest of the rescues were put on hold Sunday night while air tanks and other systems are refilled.
Journalists leave the site of the Tham Luang cave complex after Thailand's government instructed members of the media to move out urgently, in the northern province of Chiang Rai, Thailand, on July 8, 2018. The team and coach were exploring the cave after a practice game when heavy rainfall and flooding cut off their escape route out of the cave and prevented rescuers from finding them for nearly 10 days.
Thailand's rainy season began on May 26 but the cave where the boys are trapped is located in the country's north, which gets much less rain than the south.
Somboon Sompiangjai, 38, the father of one of the trapped boys, said parents were told by rescuers ahead of Sunday's operation the "strongest children" would be brought out first.
A multi-pronged rescue effort has been underway since they were found almost a week ago.
"Football's Coming Home. First Wild Boars Out", a headline on one online Thai paper said on Monday, referring to a song chanted by English soccer fans at the World Cup now underway in Russian Federation. Other divers were on guard along the unsafe first kilometer of the passageway.