They don't need to use the huge starship though. In principle they could build a dedicated space craft which is fitted on top of Falcon Heavy and delivered to L

They don't need to use the huge starship though. In principle they could build a dedicated space craft which is fitted on top of Falcon Heavy and delivered to LEO. Being smaller than Starship you should not need refueling. Astronauts arrive to LEO using F9 and dragon, where they dock and transfer to this dedicate space craft which takes them to the moon. They could even send the same kind of vehicle ahead of schedule to the moon as a backup for when the astronauts are going home.