Vladimir Komarov
Though the Soviets wanted their men on the moon first, mechanical issues caused problems. There were even some tragedies. A horrible malfunction caused Vladimir Komarov to die in 1967, and now the USSR had a black mark on its record.
One Small Step
Currently, the Americans were making up for lost time, which didn’t help the Soviets. They sent Neil Armstrong and Buzz Aldrin to the moon, and that date was July 20, 1969. They won the Space Race contest, so it didn’t matter if the Soviets had the lead before.