This sounds like a good use for "presumed sale", as covered by Robert Caldenini in "Influence".
You could go ahead and just declare the book club open, and start posting a monthly discussion thread.
Edit: when starting a book club, I have found it helps to start with a widely popular book, since folks who read it already can participate more easily. My club went through a couple very popular books, before pivoting into less known titles.
I have no idea if the book you're starting with is popular, though. I'm not as well-read as my once-having-started-a-book club might make someone assume.