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.

Wikipedia

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.