There is actually a pretty good comment about how to get to the moon without building a (4,000 ton class) moon-rocket:
Getting to the moon without a "4000 tonne" class is a parallel work, BUT neither a temporary stopgap nor an alternative/optional/additional work.
The Chinese moon program from the start envisioned two launch vehicles. One is dedicated man rated carrier, initially named CZ-5DY (all LOX/Kerosene first stags, 1600 tonne lift mass), now transformed to a CBC configuration "921" (2200 tonne lift mass). The other is a heavy lifter AKA CZ-9. CZ-9 is to deliver heavy and large sized modules to the moon surface to build long-term habitat or station. CZ-9 is NOT aimed to be man-rated initially, but may (or may not) in the future.
As you can see, the original and initial plan to go to the moon surface was never to be a 4000 tonne class, but something around CZ-5, CZ-5DY or "921". Also note, "921" can be seen as "CZ-5CBC" as it is from the same technical tree (CZ-7, 8 included) which rooted as CZ-5 as an overall program decades ago.