Every country has rare earth elements. Just google "X discovers rare earth" where X is your country of choice and you'll find articles about how they have huge deposits. The underlying problem is the processing. China has figured this out and has cornered the market. Until other countries figure out how to process these materials, China will be able to leverage this capability to their advantage.
Not every country has economically extractable heavy rare earths, resource =/= reserve. X discovers rare earth is the same as X discovers plants, and then assume every country can build a robust biofuel economy. Reminder PRC has the MOST shale deposits in the world, they're just buried very deep and economically AND technically not productive to extract at scale.
PRC's main choke hold is HeavyREE, more specifically processing of ionic clays that is GEOGRAPHICALLY SCARCE like economically extractable oil deposits, which enables economic leeching of heavy strategic rare earth AT SCALE. Think hunting whales for blubber vs drilling oil, supports entirely different tiers of proliferation and use. At scale is key, west never used HREEs at scale until PRC commoditized them by exploiting specific geology mostly limited to south PRC, Myanmar, parts of Brazil but deposits now also found in Australia because Australia has everything. So the real question is can long will it take AU+co to discover and build the entire HREE infra based on deposit types only PRC has real experience with.
It's have nothing to do with "figuring it out". Both mining and processing been figured out decades ago. But rare earth mining is disaster for ecology and western countries just don't want to pay the tall and deal with political consequences. Countries like China and Russia have advantage the they can do whatever they want without caring about protests or long term effects on population of regions where mining occurs.
There quite few talks on the topic, but you can check this one by Dr. Julie Klinger of University of Delaware:
