In fact, they are not. The US doesn't have a single operational manned space vehicle.
There hasn't been a single manned test of the Orion Space Module
There hasn't been a single test launch of the SLS lift rocket.
NASA doesn't have the resources to put even an unmanned rocket into TLI.
Claiming to build a complete manned space program from scratch in less than 3 years is a ridiculous boast.
China is years ahead of the US now in manned flight. China will return to the moon long before America and when they do, they won't claim the moon "for all mankind" ... they will claim it for The People's Republic of China.