There was lots of advance planning, debate, and strategic discussion on how to use subsequent nuclear weapons. It looks like the third atomic bomb parts (including the plutonium core) were en route to the Pacific and made it as far west as Moffett Field in California when the war ended. It was going to take only a few months to get production up to three bombs per month.
I learned this week that Oppenheimer had proposed sometime in ‘45 that Little Boy (the Hiroshima uranium bomb) could be repurposed somehow into many more weapons, but Groves refused the concept in favor of speed.
Thanks!
https://en.wikipedia.org/wiki/Manhattan_Project#Bombings
> Groves expected to have another atomic bomb ready for use on 19 August, with three more in September and a further three in October. Two more Fat Man assemblies were readied, and scheduled to leave Kirtland Field for Tinian on 11 and 14 August. At Los Alamos, technicians worked 24 hours straight to cast another plutonium core. Although cast, it still needed to be pressed and coated, which would take until 16 August. It could therefore have been ready for use on 19 August. On 10 August, Truman secretly requested that additional atomic bombs not be dropped on Japan without his express authority. Groves suspended the third core’s shipment on his own authority on 13 August.