If you are simply asking when the Soviet Union came to have a nuclear weapon, the answer is 1949. The Soviets exploded their first nuclear weapon in August of that year. However, one can argue that the Soviet Union did not really "develop" this nuclear weapon. The atomic bomb that they detonated was identical to the bomb that the United States had test exploded in New Mexico in 1945. The Soviets had not developed their own. Instead, they had used espionage to learn how the Americans had made the bomb and then they copied that bomb rather than developing their own.
One way or another, they got atomic bombs by August of 1949, causing their relationship with the United States to become more tense and dangerous.