They had some espionage information from the Manhattan Project, but they had to do the hard work themselves (and they didn't use the information optimally or efficiently, because they didn't fully trust it).

They had a very small research program during World War II. After Hiroshima, Stalin put it into a full development mode with virtually unlimited resources, including prison (gulag) labor.

They managed to get a bomb in four years by starting vigorously in 1945. By comparison, the Manhattan Project managed to get a bomb in about 2.5 years (starting vigorously in early 1943). The Soviet effort was of comparable size and scope. It was not unusually fast. Most of the US experts in 1945 guessed it would take them about 5 years, and that is about what it took — a little quicker, but not by an unreasonable amount, especially since they had already done some of the small-scale research before 1945, and they knew it could work.