Considering that the USSR had its own active space and lunar program, and landed on the moon in its own mission shortly later, they were well aware that it was not an impossibility and it's unlikely that there was any significant skepticism in government. Frankly, the second world superpower couldn't afford to brush off such an accomplishment with disdainful skepticism. Any faltering in its own efforts to reach the moon would have left it in a dangerous position in terms of technological advancement.