Crew won't be launching on Starship any time soon. IIRC the approach being taken for Nasa's human landing system (still several years away) will have the crew launch on SLS, a Starship launching uncrewed and getting topped up in-orbit by tanker ships. Crew will board in lunar orbit to descend/ascend: nobody will be on the booster-assisted part, and launching from the moon will use different thrusters situated higher-up the ship body to avoid digging a hole.

There are private flights proposed, but AFAIK there's no firm schedule. The approach to certification is similar to Falcon 9: have a long series of successful launches. (Unlike e.g. SLS or the Shuttle, which are crew rated during development).

Edit: Maybe you're thinking of Nasa's SLS rocket, which had a successful launch and is meant to be taking crew on a lunar fly-by soon (probably slipped from this year)? (SLS is orange and white with side boosters; Starship is silver and black with fins)