So the most common sentiment about the atomic bomb prior to its use was that it would change the nature of warfare in the future, not that it would immediately end World War II or that it was necessarily (in its present form) a revolutionary weapon. It was its potential that really animated the imagination of policymakers and scientists involved — they were already imagining thermonuclear weapons, smaller weapons, secret arms races, World War III, and so on. This was the part that was really going to be change in their mind — not its appearance in World War II, which would just be its introduction to the world.

Which is a really big difference from the "war winning weapon" mode of thinking about it. It was certainly the case that many of those involved hoped it would contribute to the end of the war. But they didn't think one or two uses would do it. General Groves, head of the project, wrote to Oppenheimer a few days after the Trinity test that:

It is necessary to drop the first Little Boy and the first Fat Man and probably a second one in accordance with our original plans. It may be that as many as three of the latter in their best present form may have to be dropped to conform to planned strategical operations.

Which is strongly indicative that he didn't think that the bomb was going to "win the war" in any immediate fashion.

That doesn't mean there wasn't hope of that — but the US policymakers were surprised that Japan seemed willing to surrender around August 10th, and scrambled to make sense of the next steps. Once Japan surrendered, the narrative got re-written to emphasize the importance of the bombing (and, at the time, the Soviet invasion of Manchuria; later, US accounts tended to de-emphasize that aspect of it).

There were also, of course, some people at the time, both prior and after its use, who saw the atomic bomb as merely an expedient way of expanding the firebombing strategy — using one plane instead of 500 to accomplish the same ends — and nothing "special" at all. This tended to be an attitude held by people who were involved in the bombing at a "low level" (e.g., assembling the bombs) or people who felt that giving the atomic bomb a lot of attention challenged the importance of the conventional bombing campaign (e.g. people who were involved in the US Army Air Forces and wanted them to be their own service at the end of the war).

The best book on this exact question is Gordin's Five Days in August, and it is all about attitudes towards the atomic bomb before Hiroshima, after Hiroshima but before surrender, and after surrender.