OTL to compete with the US manned Moon Program and its Saturn V rocket the Soviet came up with N1 Rocket as a launch platform for their orbital spacecraft and lander. But as it progressed the N1 rocket was unable to achieve the desired result, three test rockets were destroyed due to technical failures in fuel piping and the problem was never remedied. N1 always failed to achieve orbit whilst its US counterpart, the Saturn V was able to make a successful entry into orbit. Without having any platform to launch their orbital spacecraft, subsequently the Soviet manned Moon program faced severe setback and the US was able to proceed landing on the Moon with Apollo 12.
But now what if the Soviet was able to develop and design their rocket more carefully albeit slowly and in earlier time frame with more flight tests such that the N1 fuel piping which was deemed deemed too complicated, unreliable, and was prone to damage in transportation, could be improved or designed from the beginning to remove this problem, into an extent to allow the first N1 successful entry into the orbit? Certainly this could trigger more competitive space race from both sides.
If the N1 success continue the Soviet could certainly launch their own landing mission to the Moon, perhaps on near similar time or even earlier than the US could.
The question is what impact would this event have on the space race and the Cold War as a whole? Would the Soviet be just wasting more money than they should be? Or there would be a significant event following this landing?
I'm more interested with the technological impact this event would bring. Obviously the US would launch more mission to the Moon to compete with the Soviet, even into such extent of building a permanent Moon base. The Soviet on the other hand would also undoubtedly try to increase their presence on the Moon. The entire human space program could be more focused on higher orbit and beyond rather than just in the Low Earth Orbit as in OTL with the Mir and ISS.