It was pointed out elsewhere that there are a lot of problems with the idea of the Soviets making it to the moon first - I did see one realistic take on it on an AH website, but it required a major disaster in the US programme, the Soviets didn't pull it off till the early 1970s, and even then it was a very Soviet affair with landing multiple unmanned capsules because only one of them might work on the way back up, etc.
Not easy to have the Soviets on the Moon first, indeed. Main PITA is the insane rivalries between Glushko (prostituting his tremendous engine knowledge to whoever rocket builder is the present Politburo favorite) and the three strong pig of personalities of rocket builders - Yangel, Korolev, and Chelomei.
So much bright people, so much talent wasted.
The most balanced personality among the three is certainly Yangel but past 1960 both Korolev and Chelomei steamrolled him - plus Glusko is lurking in the shadows to crush everybody and take control - OTL it happened in 1974.
Glushko was really holding the entire space program hostage with his engines, to the point that after running afoull with him Korolev had to pick an
aircraft - turbojet / turbofan builder - Kuznetsov - to get his separate rocket engines for the N-1. And we all know how BAD this ended.
I never tried my hand at it - first because I like OTL Apollo, secondly because detailed documentation on the Soviet Union lunar program is still lacking (think NASA NTRS + NASA histories)