In spite of NASA currently backing a Gateway station and the ULA (United Launch Alliance) Space Launch System, any major new moon base construction or capabilities will depend upon the success of the SpaceX Super Heavy Starship.
SpaceX Starship will be able to land on the moon and it will be the largest lunar lander capable ship that is likely to be made by anyone other than SpaceX in the next fifteen years.
Space Launch System does not have a large lunar lander yet. In May 2019, NASA selected eleven companies to produce studies of a multi-element landing system that would be staged on the Lunar Orbital Platform – Gateway previous to the docking of the Artemis 3 crew. These are termed "transfer element" (to low-lunar orbit), the "descent element" to take the crew down to the Moon's surface, and an "ascent element" that would take them back to the Gateway. After Artemis 3, it is intended to make these systems reusable through refueling. The descent element does not exist yet.