I think its not impossible to make an authentic feeling piece thats reminiscient of a certain era. I'd definitely try to avoid using certain tropes and writing style choices of that era, since some tropes have probably not aged well. Premise, tone and setting though are definitely the major points you'd want to think about.
It's a good idea. Certainly a fun one to research. By research, I mean watching lots of old movies. :)
I tried back in 2018 to write a story about a boy who saw the original Invasion of the Body Snatchers (1956) in the theater and convinced himself his neighbors were aliens from another planet. Sadly, I was never able to come up with a draft I was happy with. I hope to come back to it some day. Heck, maybe I just did.
You know, when I come up with an idea, I write it down. That, for me can take a few different shapes: a few sentences explaining the idea, a few paragraphs or some dialog to place somewhere in the story if I actually get to writing it, or a full outline of what, where, how, and all that jazz.
Whether I finish the story or not, I got some good practice, and that, for me, is what writing is all about. It doesn't have to always be about beginnings, middles, and ends.
Sometimes it's just playing with words and ideas and imagination.
Ya know, dancin' around in my head and seeing what my brain pukes up when it gets dizzy. d:
Oh, yeah, I almost forgot. Good luck with your idea. It really does sound like fun. And thanks for reminding me about an old story. I think I'll go dig it out of my files and see what I think of it now.