For the 27 September date, a "70-minute launch window opens at 11:37 am EDT," while the mission would end with an ocean splashdown of the Orion capsule on November 5.
A potential next date comes on 2 October.
The Artemis 1 space mission hopes to test the SLS as well as the unmanned Orion capsule that sits atop it, in preparation for future Moon-bound journeys with humans aboard.
Once launched, it will take several days for the spacecraft to reach the Moon, flying around 60 miles (100 kilometers) at its closest approach.
One of the trip's main objectives is to test the capsule's heat shield -- which at 16 feet (five meters) in diameter is the largest ever built -- when the ship re-enters the atmosphere.
The next mission, Artemis 2, will take astronauts to the Moon without landing on its surface, while the third -- set for the mid-2020s -- would see the first woman and person of colour on lunar soil.
NASA wants to build a lunar space station called Gateway and keep a sustained presence on the Moon to gain insight into how to survive very long space missions, ahead of a mission to Mars in the 2030s.