Soviets had no interest in going to the moon (yet) and were more focused on living in space before going outside earth’s orbit. The US was waving it in public on its own
Not seeing how building a rocket to compete with Saturn V means they were also racing to the moon
From the references of the wiki article on the N1 rocket
https://web.archive.org/web/20161031200800/http://www.starbase1.co.uk/pages/n1-project-history.html
Salyut and Mir prove the Soviet’s focus was on manned missions in low earth orbit and not the moon, and considering nobody has gone back to the moon since they’ve made the right call
You don’t need anything that powerful for earth orbit. Salut and Mir launched on much less ambitious rockets. They became the focus after the moon race was decided.
The N1-L3 version was designed to compete with the United States Apollo program to land a person on the Moon, using a similar lunar orbit rendezvous method. The basic N1 launch vehicle had three stages, which were to carry the L3 lunar payload into low Earth orbit with two cosmonauts. The L3 contained one stage for trans-lunar injection; another stage used for mid-course corrections, lunar orbit insertion, and the first part of the descent to the lunar surface; a single-pilot LK Lander spacecraft; and a two-pilot Soyuz 7K-LOK lunar orbital spacecraft for return to Earth.
You build an N1 or Saturn V to go to the moon.
Had the N1 launched without incident, the Soviets were on target to get a man on the moon first. When the Soviet Union fell all the details of the program became available.
The US wanted to beat the Soviets at space, and the reality was when it came heavy lifting rockets the soviets were way, way ahead. The moonshot was a different problem that would require a different solution than simply “bigger rocket,” so the US made that the goal. They weren’t sure they could beat the Russians to the moon, but they knew they couldn’t beat them in a lifting contest for something like a space station.
