The first one won’t be crewed, and there’s no way that’s going to be ready by 2022. So 2024 will be unmanned. Maybe 2026 will be the first crewed test mission, but 2028 is more likely. But we’re still talking aspirational Elon-time. If I were betting money, I’d say the 2030’s is more realistic.

Note that they have done zero work on building a anything other than the rocket body to get there. Making the interior volume habitable for 2 years of interplanetary travel is going to be non-trivial.