SpaceX President and COO Gwynne Shotwell described the SpaceX moon timeline at the IAC (International Astronautical Congress) 2019.
First Starship earth orbital flight within 1 year
Land on moon before 2022. They want to stage cargo with an unmanned mission.
Trip around the moon (crewed) in the 2023 timeframe. This with the Japanese billionaire.
Moon landing by 2024
Those are aspirational targets.
Starship is the vehicle of dreams. It will go to orbit, moon and Mars.
Gwynn did emphasize that the current most important SpaceX job is the crew Dragon for NASA.