The first boy rescued exited the cave 5:40 p.m. local time, followed by three of his team members shortly after.
Water levels have a massive effect on the difficulty of the rescue operation.
After considering a "bouncy castle" air tube that the kids might be able to wriggle through to safety, Musk and his team settled on the idea of building a kid-sized submarine, equipped with external air tanks.
The extraction of those remaining is expected to take another two to four days, depending on conditions.
Elite divers began a rescue mission Sunday, successfully escorting four of them out, and were aiming to extract the others swiftly before fresh monsoon rains made escape impossible.
In the week since the team was found alive, expert climbers, divers and Thai Navy Seals have mulled contingencies ranging from drilling an escape route through the mountain to waiting out the monsoon season and spending months inside the cave.More news: Somerset drunk gulls found 'stinking of alcohol'
Narongsak told reporters earlier Sunday that the boys would be brought out one by one and that it could take at least 11 hours for the first person to be rescued.
Falling oxygen levels, and with numerous boys not able to swim well, present further risks should they panic as they are guided slowly through the pitch-black waters.
The California tunnel company run by Musk is continuing to maintain a presence at the Thai cave where several boys and their soccer coach are awaiting rescue.
On July 6th, former Thai Navy diver, Petty Officer Saman Gunan died while helping deliver oxygen to the team.
Two helicopters wait near the cave for more evacuations of the boys and their soccer coach on Monday.
An official from Thailand's Forestry Department said that despite heavy rains overnight on Sunday, "the water levels are still stable".
NowMedia will update this story as more information becomes available.More news: Spain manager odds: Roberto Martinez and Luis Enrique among favourites
Sustained heavy rains could make the water rise to the shelf where the children were sitting, reducing the area to "less than 10 square meters", he added.
The boys who have already been rescued have been rushed to hospital for 48 hour observation following their ordeal.
The boys have been trapped in the Tham Luang Nang Non cave since June 23 when they and their coach entered and were then cut off by flash flooding. However, they ended up starting the rescue effort a few hours earlier than planned.
This is a hugely high-profile rescue attempt and Thailand knows the world is watching.
One of the boys, identified as Tun, wrote: "Mom and Dad, please don't worry, I am fine".
Global rescue teams from the U.S., China, Australia and Europe are stationed along tunnel walls from the entrance of the cave to chamber 3, a safe command center inside the cave, to support the extraction.
Musk posted videos on Twitter of the aluminum sub being tested at a swimming pool Sunday midafternoon California time. I've told Yod to get ready to take me out for fried chicken.More news: ZTE replaces entire executive team to comply with technology ban deal
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