The Manhattan Project planned a massive "Publicity" blitz to inform the (global) public about the nature of the nuclear weapons they had just created. This included political press releases (from the President and Secretary of War), pre-written newspaper articles (written by "embedded" reporter William Laurence of the New York Times) that were deliberately circulated without copyright protections to encourage re-use, and, a few days after Nagasaki, a book-length technical history of the project (the Smyth Report). They did all of this with the dual intention of informing and withholding — they were very selective about what they released, but they released a lot, and emphasized that their version of the story was the maximum of what could be said about it for the time being.

So the fact that the atomic bombs were powered by enriched uranium and plutonium would have been known well in advance of Notorious coming out. As for "how much" an average person would know, that's hard to estimate (we have some poll data but it isn't of a "how much do you know" sort, it is of a "what is your opinion on the danger" sort), but it was a major news story and so probably had a pretty high saturation among the public. My usual point of comparison for things today is to note that lots of the public know technical names even if they don't understand the details — if the Higgs particle was mentioned as a MacGuffin in a show (as it is on the Netflix show Dark), I suspect most people would have a vague sense that it is a real thing, even if they don't really know much about it (other than perhaps its silly "God particle" name).

As for Hitchcock — he did start the film prior to August 1945, and uranium was indeed in the plot prior to that, according to that ever-reliable source, Wikipedia. Apparently the people who had read the script were confused by it. The fact that uranium could be connected to atomic bombs and atomic power was known to the literate/educated public before Hiroshima. There were breathless articles — some written by the same Laurence who became embedded with the Manhattan Project, and were the reason they brought him in to it — about its potential as an energy source. But it would have been considerably more obscure than after Hiroshima.

Hitchcock apparently claimed to have been followed around by the FBI or other security agents. I can't confirm that he was, but it would not have been impossible: the Manhattan Project security forces spent a lot of time investigating apparent leaks or rumors, and did try to silence creatives and artists who were speculating about atomic bombs and uranium (with limited success). So if they had gotten wind of a film with uranium as a plot device, they probably would have investigated it to find out whether Hitchcock had gotten leaked information, or whether his work was (in the span of the war) likely to draw unwanted attention to the issue.

It doesn't sound to me like Hitchcock had any kind of "inside source" but it's not impossible that he might have heard a loose rumor. There were many going around, and supposedly just prior to Hiroshima it was an "open secret" among the Washington, DC, press corps that the US was going to use some kind of new super-weapon against the Japanese. Obviously it is easier to make a positive attribution of such a rumor after the fact (it is a form of confirmation bias; there are always swirling rumors, many of which turn out to be false) but it gives some indication of the difficulty (nay, impossibility) of keeping a project of that size and scope totally secret, especially when it was based on previously-published scientific research (uranium fission was discovered in late 1938).

My book — Restricted Data: The History of Nuclear Secrecy in the United States — comes out in April from University of Chicago Press and has a LOT on the issue of World War II-period rumors, leaks, and public information campaigns in the first third of the book.

I asked a similar question titled How did the average Joe come to grasp what an atomic bomb really was after the bombings of Japan? and got an excellent answer from u/restricteddata.

It's an interesting subject, the answer to my question focuses mostly on the aftermath (and nothing about Hitchcock), so definitely could be more to say!