You must have seen this kind of scene in some media or other: a film noir-style private eye is napping or brooding at his desk. The door opens and in walks a vampish dame; she’ll likely be richly dressed and there may be a view on her from her legs upward. She comes in and says she has a case for him, and the story develops from there. I’ve seen this situation in enough works to surmise that we are dealing with an established trope. Not surprisingly, it can be played as parody; a good example is the few arcs in the comic strip “Calvin and Hobbes” where Calvin imagines himself as the cynical, Byronic PI “Tracer Bullet”; in one arc the dame that walks into his office is revealed out-of-imagination to just be his mother; in another arc, it was IIRC his imaginative stand-in for his classmate Susie Derkins.
Where does this trope originate? Is it by any chance the film “The Maltese Falcon” (or perhaps a scene in the novel that it was based on?) The opening scene of the film (see here) indeed shows such a scene, though admittedly, the woman with the case (Brigid) doesn’t seem as vampish (think Veronica Lake-, Lauren Bacall-, or Jessica Rabbit-like) as in the later spoofs and parodies that I’ve seen.
The book The Maltese Falcon predates the movie most people think of by that name by eleven years.
Bulldog Drummond has pretty much the same trope from 1920, though the woman contacts him by mail.
In a sense, a prototype was Wilkie Collins’s The Woman in White has the action started by meeting the title character, though it doesn’t involve an actual detective.
The general concept of “a dame with legs that go on for days” can be found in multiple books. I, too, would guess that it originated in the books, and then hopped over to movies.
The private eye as we know him (her came later) is generally attributed to Carroll John Daly’s story “Three Gun Terry”, in the May 15, 1923 Black Mask magazine. Dashiell Hammett’s Continental Op followed in 1923. The magazine surged in circulation and dozens of writers contributed private eye stories, mostly imitating Daly and Hammett and then each other so they all read kinda the same. “The Maltese Falcon” started serializing in the magazine in 1929.
So the trope definitely dates back to 1929. My guess is that it started no later than 1925, because Hammett’s story is almost a parody of the genre and the vamp would be part of the setting.
I’m not an expert but I’ve read a fair number of early detective stories. If there’s a female protagonist she’s almost always attractive so you won’t have a definitive “first”. IMO the incident that turned it into a trope is The Maltese Falcon. Miss O’Shaughnessy is a bombshell that catches even Effie’s eye and is the iconic femme fatale.
She was arguably a vamp, but she wasn’t the one to walk into Holmes’ “office”. For a woman coming to Holmes with a case, there’s the earlier example of Mary Morstan coming to see Holmes in The Sign of the Four.. Morstan probably wasn’t a “vamp”, although she did end up marrying Watson.
And before Ms. Morstan, Holmes did a case for Mrs. Cecil Forrester (not the wife of the author of that name), although it’s not clear how those two met.
I watched No Clue a few days ago, a 2013 Canadian film that both lampoons and pays homage to this trope. I had never heard of the movie before. Comedian Brent Butt’s character, Leo, does his best to be a hardboiled gumshoe, but is soon in over his head… or maybe he isn’t? Amy Smart plays the vamp, Kyra. I was chuckling all the way through it.