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.
SpaceX Starship could have its orbital prototype versions flying by the end of this year and it should reach orbit within a year.
SpaceX Starship will weigh 85 tons empty and about 1350 tons (2.95 million lbs). Apollo’s Lunar Module (LM) is the heaviest vehicle to have ever landed on the Moon and it weighed maximum of 5500 kg (12,100 lb) at landing (Apollo 17). The SpaceX Starship will be able to take 10-50 times more payload to the moon than the Lunar Module.
The main technology that will take us far beyond what was done with Apollo is SpaceX Super Heavy Starship.