The late John Coster-Mullen, a fantastically interesting character (a truck driver who became an important researcher into the history of nuclear weapons, and a friend of mine for some 15 years before he died in 2021) was the one who determined pretty conclusively that the Little Boy bomb worked by firing a cylinder of 38.53 kg HEU into a "target insert" of 25.62 kg HEU. Wikipedia has a basic diagram of the idea based on his work (he constantly revised his exact diagrams up until his final year of being sick, so it doesn't reflect exactly what he concluded by the end, but the differences were pretty minor to your question).

So the big hollow piece (60% of the total mass of fuel) was fired into the small thin piece (40%). Little Boy was "a girl," as John put it.

Prior to John's work, everybody assumed it worked the opposite way, including Rhodes. John basically convinced everyone that they were wrong, a rare thing. The idea was first broached to John while he was talking with Harlow Russ, a project participant, who told John in 1994, "You knew the projectile was hollow didn't ya?" Which neither John nor anyone else seems to have known. John then worked to substantiate this through interpretation of bits and pieces in various documents.

Once he put out the idea, it became pretty easy to find confirming evidence, once one thought to look for it. I found a document that John called his "smoking gun" which describes how they put a very thin cadmium plating on "the inner cylindrical surface of the projectile and the outer cylindrical surface of the target," which to me implies a hollow projectile (the idea being, presumably, to absorb some low level of neutrons until the thing was fully "mated" to prevent predetonation). I also found a reference in an oral history that the reporter William Laurence (who was at Tinian) did with Columbia University in 1964 in which he described the bomb internal bits as "the largest part was on one end attached to the gun mechanism, and the other part was on the other end," and explained that the large part would be shot into the other end. Which, of course, one might suspect (if one didn't know better) that he had it mixed up. (In that same interview, he gives pretty accurate recollections of the critical masses of both atomic bombs, which is rather remarkable. Though he also called the bomb "lean boy," so memory isn't everything.)

Anyway, all of which is to say, people became convinced it was true rather quickly after John suggested it was and shared his evidence for it. Rhodes today agrees with John's description, but that is not what was in his 1986 book. John's book is much more than this simple revelation (it goes into considerable technical detail about both atomic bombs, with some information gleaned from cameras he snaked inside of bomb casings in museums), but that revelation was always the jewel in his crown. His relentless research is what made people believe him, though. Anyone can say they think atomic bombs are designed one way or another; convincing other people is the harder thing.

John's self-published book, Atom Bombs, is hard to get ahold of since his death. I am hoping to try and negotiate a university press to publish a "final," edited edition of it; he updated it regularly, so even copies that are out there are not necessarily his most "up to date" versions. Unfortunately this has taken a lot longer than I had hoped (for about a million reasons, many relating to my own life being often quite busy).