Starship is a SpaceX rocket reasonably late in the development cycle, and is planned to land on the moon in an uncrewed demonstration flight no earlier than 2024, and with people during NASA's Artemis 3 mission no earlier than 2025. According to the plan this will be the first mission to land people on the moon since Apollo.
SLS at this point is not planning on launching a vehicle that lands on the moon, instead just a very very expensive taxi to a starship in lunar orbit which could have easily carried the astronauts there itself...
Pretty sure it's untried. Theoretically easy, just like launching starship is theoretically easy.
Of course it's more challenging.
And it does matter if there's more fuel, you have to have valves and pipes that won't freeze after lengthy contact with cryogenic fuel. And you need larger pressure vessels, which scale in volume differently from surface area. It's not at all the same whether you move one ton or a hundred.
Regardless of the dates, Artemis using starship as a lander seems practically guaranteed at this point, so SLS really is relegated to the role of unnecessary taxi...
If history is any guide and they haven't missed any big blockers though, then they'll get there - but I think a 10 year horizon is probably a reasonable expectation.
Several Moon missions were launched on commercial rockets. Even tiny RocketLab launched one: https://en.wikipedia.org/wiki/CAPSTONE