I've never seen anything that indicated that any substantial number of people thought they were being lied to. One should remember that the physics underlying the bomb (nuclear fission) was known before the war began, and that the list of eminent scientists working on the project was extensive. The Smyth Report, published a few days after Nagasaki, treated the subject of how they were made and worked in enough technical detail to be compelling to anyone with some technical background (part of its explicit purpose was so that technically-minded people — engineers, for example — could understand the new weapon and explain it to others). A great publicity barrage followed the bombing of Hiroshima, explaining what the bombs were, how they worked (not in detail, of course), who made them, where they were made, etc. We could think of this as in part fleshing out the backstory narrative as part of making it more evident how this new thing just suddenly appeared — the publicity was directed at the Japanese as well.

The notion of a giant conspiracy between the government, the scientists, the photographers, etc. — just not the sort of thing you'd see in 1945. (This is not to say that there weren't what we'd call conspiracy theorists in the 1940s, but it was more along the lines of "FDR knew about Pearl Harbor" not "every scientist is faking evidence.") One can find someone who believes anything but there is no evidence that anyone of significance or any people in great numbers doubted the existence of the atomic bomb.

Also, separately, the notion that atoms contained lots of energy bound-up in them, that could be released in various ways, was very well-established in popular culture by the 1940s. Even the notion of an "atomic bomb" was a well-known science-fiction staple since the late 1910s. So it was not as jarring an idea as one might imagine. If scientists announced that they had created a wormhole tomorrow, and provided data to prove it, many people would have some idea of what they were talking about, even if their knowledge of what that meant was primarily mediated through works of fiction.

There is more that could be said about public opinion (there were polls taken about whether people thought atomic bombs would be used in future wars, etc.), but it seems like the above is what you are getting at.