It's the wrong question though! The US is sitting on piles of rare earth deposits—it still doesn't mine them. It can't compete on pure cost with the mining industry in China. It's discussed extensively (e.g. here[0]) that the mining, and particularly chemical processing of ores, is labor/resource-intensive, expensive, and hazardous to ecology and to humans. It has nothing to do with the raw availability—these are super abundant ores, not rare at all, despite the name.

Jack Lifton in [0] adds the perspective that rare earth processing involves a large amount of institutional knowledge, that would take time for the US to reacquire, since we forget everything when we stopped mining many decades ago. While in the interim, China has spent its time as the world's rare earth monopoly optimizing the chemical processes, widening their moat. It's like the manufacturing question, where's it about institutional knowledge and industrial ecosystems—nothing at all like oil/gas where it's solely about where the minerals are.

[0] https://news.ycombinator.com/item?id=43953272