Given current levels of technology, this would require docking with a series of space tugs. Not impossible, but Blue Origin is the only organisation working on this at a meaningful scale.
There was also Nautilus-X which never made it beyond the concept stage.
Mir and the ISS were built this way and the Space shuttle, Dragon, and Soyuz have/had no problem docking with the ISS.
If you feel constrained by the size of the Falcon Heavy fairing the now defunct Bigelow Aerospace launched several prototype inflatable habitats that apparently tested well in LEO.
Combine this with a lunar cycler[0] orbit and you could keep reusing the same craft over and over and expanding to it if you want to ferry the astronauts to the moon.
You'll note that everything I'm describing requires existing technology and very proven techniques (except maybe the inflatable stuff) but the thing it doesn't require is a giant rocket like SLS or Starship. I'm not saying that we shouldn't build machines like that, it's just that they really aren't needed for a mission like this and I question why something like SLS was built in the first place.
[0] https://en.wikipedia.org/wiki/Lunar_cycler