From the Wikipedia page on the test:
In TTL, the test fizzles and the plutonium is lost. It is unclear why the bomb does not detonate and people need to start trying to figure out what happened (and obtain more plutonium in the process).
This leaves the US with one bomb which is expected to work. It is dropped on Hiroshima as IOTL. The Soviets then declare war on Japan. Now what? Remember that Japanese officials naturally assumed the US had only one bomb.
The code name "Trinity" was assigned by J. Robert Oppenheimer, the director of the Los Alamos Laboratory, inspired by the poetry of John Donne. The test was of an implosion-design plutonium device, informally nicknamed "The Gadget", of the same design as the Fat Man bomb later detonated over Nagasaki, Japan, on August 9, 1945. The complexity of the design required a major effort from the Los Alamos Laboratory, and concerns about whether it would work led to a decision to conduct the first nuclear test. The test was planned and directed by Kenneth Bainbridge.
Fears of a fizzle led to the construction of a steel containment vessel called Jumbo that could contain the plutonium, allowing it to be recovered, but Jumbo was not used.
In TTL, the test fizzles and the plutonium is lost. It is unclear why the bomb does not detonate and people need to start trying to figure out what happened (and obtain more plutonium in the process).
This leaves the US with one bomb which is expected to work. It is dropped on Hiroshima as IOTL. The Soviets then declare war on Japan. Now what? Remember that Japanese officials naturally assumed the US had only one bomb.