NASA plans to launch Artemis I Moon mission in February 2022

That's as long as testing goes according to plan.

NASA Orion capsule stacked on SLS rocket for Artemis I Moon mission (NASA)

You'll have to wait a while longer for NASA's Artemis I mission. notes NASA now expects to launch the uncrewed Artemis I flight test in February 2022, with the liftoff window opening as soon as February 12th. The Orion capsule has been stacked on top of the Space Launch System rocket, and blastoff is now mainly contingent on testing.

That testing could take a while, however. The space agency plans tests for interfaces, engineering, communications and the countdown system. The most important test is effectively the "Wet Dress Rehearsal," when the Artemis I crew will try loading and unloading the propellants several weeks before launch. NASA won't set a firm launch date until after a successful rehearsal, so you won't get definitive timing for a long while.

Artemis I will send an Orion capsule with a sensor-equipped "moonikin" around the Moon (plus organ- and bone-like "phantoms") to study acceleration, radiation and vibration during the journey. Artemis II will carry a human crew. NASA hoped to land people on the Moon in 2024, although budgetary concerns and the fight over lander contracts have cast doubt on that target.

A successful Artemis I mission would nonetheless represent an important milestone. It would demonstrate the viability of both Orion and SLS. More importantly, humans would take one step closer to venturing beyond Earth's orbit for the first time in decades.