As I underestand, it was not purely confidence, it was also that there was a major war going on and the expected production rate was low, so the risk of failure in the field was judged a lesser cost than the using up another bomb in testing.
It took basically the entire Manhattan project to create enough U-235 for that single bomb dropped on Hiroshima. There was no more U-235 coming, at least not any on a scale or timeline for the war.
It probably would have been more efficient to dilute the U-235 into reactor grade and use it to manufacture weapons grade Plutonium. However at the time the U.S. only had two bombs (the ones dropped on Hiroshima and Nagasaki) and it was probably judged politically expedient to drop two instead of one.
Well, there were basically a few different strategies to produce U-235 during the war. For Hiroshima, most of the Uranium came from a very temporary but quicker to setup using an electromagnetic process at Y-12 in Oak Ridge, and that ended with the war. The gaseous diffusion plant at K-25, also in Oak Ridge, came online in 1945 and ended up being the main enricher for much of the cold war; it was a construction marvel, and the fact it was built in 2 years is still remarkable. The US definitely would have been ready to produce many more in not too long for the war had it been needed.
All of these processes were brand new at the time and mostly untested. Plutonium enrichment at the Hanford site used a reactor design that was validated well into the construction of the site. The Manhattan project already had a lot of risks, and they weren't going to attempt chaining projects for something unproven. Real experiments came after the war.
