My best guess is late April at the earliest depending on any further delays to the process. Given the YEARS of delays the vehicle has experienced a few more weeks won't hurt. NASA definitely isn't on the same type of timetable or efficiency that SpaceX has been on. I'm curious as to which will actually launch first - SLS or Starship (tentatively for May)?
Now that the SLS is being rolled out to the pad they have some additional testing to do (roughly a week) and then complete a wet rehearsal which should take about 2 days. Then after a short period (est. to be several days) the SLS will be rolled back to the assembly building where they will remove the sensors, recharge batteries, and run final checks. NASA will commit to a launch date following the wet rehearsal. Once complete they will roll it back out to the pad and roughly a week later will launch the unmanned spacecraft.
https://www.nasa.gov/feature/nasa-readies-rocket-for-artemis-i-wet-dress-rehearsal
Now that the SLS is being rolled out to the pad they have some additional testing to do (roughly a week) and then complete a wet rehearsal which should take about 2 days. Then after a short period (est. to be several days) the SLS will be rolled back to the assembly building where they will remove the sensors, recharge batteries, and run final checks. NASA will commit to a launch date following the wet rehearsal. Once complete they will roll it back out to the pad and roughly a week later will launch the unmanned spacecraft.
https://www.nasa.gov/feature/nasa-readies-rocket-for-artemis-i-wet-dress-rehearsal