Let’s say the Soviet space program successfully put a man on the moon, surprising the Apollo program planners…….
What happens after that?
Does America go to Mars? Set up a moon base?
How would this damage america’s prestige?
I know you’d need a POD quite early, perhaps around the early 1950s…..
You're definately going to need a POD set in the early-mid 1950s for the SU to be able to put a man on the Moon. Where LOX/LH2 is taken seriously and developed, making it possible to use it by the 1960s. This would provide them with the TLI capability neccesary to perform a serious Manned Lunar Mission, in OTL, their design was far too marginal, with no upgrade capability. Selecting either the UR-700 or R-56 over the N1 would also be a major boon since they had real performance upgrade ability, as opposed to the N1.
The US would most likely set up either a permanent or semi-permanent Lunar Base, being within their budgetary capabilities, which the SU would quite probably lack the financial resources for.
With the Lunar Base at least, NASA could claim that they are doing real scientific research, repairing any damaged pride & prestige - assuming that the Soviets had been first. If not, it would help it further IMHO.
Mars is still unlikely since 'Battlestar Galactica' was still the dominant ideology at the time. Until 'Mars Direct' or something along those lines is developed, you can forget about any manned mission to Mars.