How about right on the Home Page! A relevant customer story is extremely compelling to your visitors.
Let Cauzal AI fetch the most converting example and promote the story. It will have 2 effects: if your visitor is not ready to convert, they might follow the link and learn more about your product through this success story. But it might also be the piece of information they need to request this demo right away
My personal favorite: use it as a H1 or H2 on your home page, right next to the CTA