The West (+Japan), led by the USA, is pretty far ahead of China.
Trump established (to the chagrin of the left)
"the Artemis Program" back in 2017. Canada, Japan and the European Space Agency have all joined in and a dozen other countries want to participate in the future. First manned flight around the moon is next year, followed by a space station orbiting the moon, and a "permanent" presence on the lunar surface by 2029.
Of course, since it was Trump's vision, NASA will find a way to cancel it.