Exactly. Simply having enough fissile material for a bomb was a huge limiting factor for building a bomb. It took several years of refining for the US to have enough for the Trinity Test, Fat Man, and Little Boy. Any physicists in Japan at the time had to have known that fissile material was a limiting factor, given that the theoretical concept of an atomic bomb was well-known physics by the time. The second bomb was to prove Japan couldn’t count on the US having exhausted all their fissile material on the first bomb.