The project met its deadline which, if it had been missed, Musk had said would have cost him "probably $50 million or more".
Eight members of the soccer team, ages 11 to 16, and their 25-year-old coach remain trapped in the cave. They were found in the cave on Monday, after spending nine days trapped underground.
Over the last couple days, Musk posited possible ways his companies could help in Thailand: "I suspect that the Thai govt has this under control, but am happy to help if there is a way to do so", he wrote on Twitter.
The boys became trapped in the cave two weeks ago after water rose and cut them off.
He has now designed a plan to help save the boys, and he said engineers from his companies would travel to Thailand on Saturday.
Musk has been following the story of the soccer team, tweeting his thoughts and offering to assist the Thai government in any way he could over the past week. On Thursday, a former Thai Navy SEAL fell unconscious while swimming through the cave and could not be revived. The billionaire engineer is now in talks with Thai authorities to establish how the resources at his disposal - including those associated with TBC and SpaceX - could help with the cave rescue.
He also proposed installing a 1m diameter nylon tube and inflating it "like a bouncy castle" to see if that would clear the water and provide a tunnel that the trapped boys could simply walk through.
Another SpaceX engineer was already in Thailand and will also help, Musk tweeted.
Short notes scribbled by each schoolboy on smudged, yellowish paper showed both humour and homesickness as they sought to reassure their relatives they were in good spirits.
"The water level may rise to the area where the children are sitting and make the area less than 10 square metres", he said, citing estimates from cave divers and experts.