There was such a race to be the first to land on the moon between the US and USSR, After the US landed, we flew more missions and landed a few more times, Why did USSR stop? Why hasn't any other country tried to achieve this and explore another area of the moon? Technology is far superior to what it was in the 60s and 70s, why don't we continue to make trips to the moon and setup a station like the ISS?
Any nation that wanted to go to the moon would have to lay out a fortune developing the appropriate infrastructure. The Apollo program cost the United States well over $100 billion in current dollars, and that's for a nation that already had an established space launch infrastructure and trained astronaut corps.
Developing a manned spaceflight program takes time. It took China 11 years to move from authorizing manned spaceflight to their first manned flight, and that's using updated technology while still cheerfully exploiting American and Russian research and engineering to the full.
These programs are hard. It's not just a matter of buying an Acme Saturn V hobby kit and fueling it up. You have to have a wealth of experts, a deep institutional commitment and resource base, and years of dedicated effort.
And it suffers from diminishing returns. No nation is going to get the prestige boost the United States did from landing on the moon for the first time. No nation needs a prestige boost of that magnitude, since no one is locked in a titanic Cold War. And as the Apollo missions made plain, the only return on a moon landing is prestige - unless you want to keep doubling down on expense and commitment until you're building a moonbase, at which point you can start refining fuel for hypothetical future fusion plants.