A flash flood blocked their way out and parts of the cave remain submerged in water, even as rescuers frantically work to drain it with industrial pumps. Over the past couple days, Musk posited possible ways his companies could help in Thailand.
He said: "Boring Co has advanced ground penetrating radar & is pretty good at digging holes".
Officials say the group are being taught how to use diving masks and breathing apparatus.
He pointed out that any drilling process could take months, likening the situation to the 2010 mine rescue in Chile that took 69 days to get the stranded miners to the surface.
"We are at peak readiness".
Narongsak ruled out any rescue attempt for Saturday, saying the boys "cannot dive at this time".
To escape, the children must dive through dark, narrow passageways sometimes no more than two-feet (0.6- meter) wide, that have challenged some of the world's leading cave divers.
More heavy rain is expected at the weekend, which is set to complicate the rescue effort. "But we can't wait for the rain".
"Some (of the chimneys) are as deep as 400 metres. but they still can not find their location yet", Narongsak Osottanakorn told reporters, adding the mission lacked the technology "to pinpoint where they are staying".
The first fatality of the rescue effort, he died while placing oxygen canisters along the route to where the boys and others are sheltered.
Four expert cave divers from the United Kingdom will guide 12 boys and their soccer coach out of the flooded Thai cave they are trapped in, with support from Thai navy seals, authorities said. He was found unconscious around 1 a.m. Friday and transferred to a hospital but was pronounced dead on arrival.
Narongsak, the provincial governor, said crews were looking for shafts and sinkholes that could offer a way to drill into the rock face.
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Any attempt to rescue the boys trapped in the cave will be extremely hard.
The diver was identified as Saman Kunam.
A dozen Australian defence and police specialists have joined in the rescue. A video surfaced Friday of him waiting to board a plane from Bangkok to Chiang Rai, announcing proudly that he was going to "bring the kids home".
Musk's tunneling startup Boring Co. could potentially make available its massive drills or excavation expertise, but such an approach could be too risky for this mission.
"Despite this, we will continue until we accomplish our mission", Arpakorn vowed.
Officials say they have a window of up to four days before rains will make the rescue more hard.
"At first, we thought the children could stay for a long time ... but now things have changed, we have a limited time", Apakorn Yookongkaew told reporters.
While the oxygen level had stabilised he warned levels of "carbon dioxide are another factor" in considering when to move the group - in addition to impending rains which could cover much of the muddy ledge on which the group are sheltering. Four navy SEALS are stationed with the boys to monitor their health, provide food to them and check on oxygen levels.
"We are ready. The boys are ready and strong enough to come out".
However, the official in immediate charge of the operation, Gov. Narongsak Osatanakorn, indicated at a news conference that if heavy rains started and appeared to be causing flooded areas in the cave to rise again, divers would try to take the boys out right away.
The governor has said the 13 may not be extracted at the same time, depending on their condition.