The issue is cadence. SpaceX is the king of cadence with Falcon 9, but if it takes >10 Starship Tanker launches to get all that excess mass of Starship HLS to the moon... prior to boil-off of the Starship HLS... holy crap, this is really hand wavy.

Even SpaceX will have a really hard time launching ~10 Tankers in the time required. What are the lower and upper bounds of that time required? Nobody knows. But, if it's less than many weeks, it's gonna be tough. That's ~weeks of HLS on orbit, getting refueled, with boil-off occurring.

SpaceX has many things correct, except for the vehicle size and design, as far as HLS goes.