Is there any reason to doubt that the Chinese will get (back) there first?
Sure. It’s not easy to do. I think odds favor China right now, but it’s far from a done deal. Anything from geopolitics to internal politics to technical hurdles could interfere (ditto with the US and everyone else of course).
Not first. Seventh.
The successful manned moon landings so far:
1. United States of America
2. United States of America
3. United States of America
4. United States of America
5. United States of America
6. United States of America
Now we're watching a riveting race for 7th place.