The boys and their coach, whose team is known as the Wild Boars, became stranded when they were exploring the cave after a practice game on June 23.
Early today, leader of the operation Chiang Rai acting Governor Narongsak Osottanakorn announced that 18 divers had entered the cave to rescue the boys.
A source inside the Chiang Rai Prachanukroh hospital where the boys are being kept said their condition was "not bad" but said doctors were watching for signs of emerging conditions such as hypothermia. It takes several hours.
Authorities had looked at many different ways to save the boys and their coach.
Foreign elite divers and Thai Navy SEALS on Sunday morning began the complex operation to extract the 12 boys and their football coach as they raced against time, with imminent monsoon rains threatening more flooding that would doom the mission.
Meanwhile rescuers fed a kilometres-long air pipe into the cave to restore oxygen levels in the chamber where the team was sheltering with medics and divers. Officials did not immediately comment.
The mission is seeing trained divers guide the boys and their coach to the mouth of the Tham Luang cave system through a treacherous maze of dark passageways. However, it only took 7 hours and 40 minutes.
The mission was only launched on Sunday morning because floodwaters inside the cave were at their lowest level in days.
Rescue workers along the main road leading to Tham Luang Nang Non cave as the first 2 ambulances carrying 2 boys pass by on July 8.
Meteorologists say there is a 60 per cent chance of further rain on Monday.
The next operation for the rest is set to resume in 10-20 hours, with officials and volunteers buoyed by the fact that their method of rescuing the boys by diving has been successful so far, he said.
Musk tweeted that he was working with a team from his Space X rocket company to build a "tiny kid-size submarine" to transport the boys.
The four boys rescued Sunday are recovering in a nearby hospital and are yet to see their parents.
"Today was the best day, the best situation in terms of the weather, the health of the boys, our water management for our rescue effort", the governor said. Sam Teller, spokesman for Boring Co., said Sunday that the company has four engineers who are "offering support in any way the government deems useful".
The Tesla CEO has designed an escape pod as he lends a hand to the complex rescue effort.
Authorities in northern Chiang Rai province began the unsafe mission to bring out the 12 boys and their coach earlier on Sunday.
The rescue mission has faced a ideal storm of obstacles since it began, including monsoonal rains, a lack of oxygen in the cave and the fact that numerous boys trapped inside don't know how to swim let alone dive.
The mission to save all the trapped is a race against the clock with heavy rain expected this week which would again flood the tunnels with fast-flowing, rising water.