As an instructor, I only require textbooks if I really expect students to use them. But waiting to get the syllabus is a good idea - I often say on there that a previous edition of the book will also work (and those are often much cheaper). I’d be disappointed if students were waiting until the 10th day to buy the book.
Sometimes I notice at the book store that the store has ordered the study guide that goes along with the book even though I did not request it. I don’t like it when they do that. That’s why looking at the syllabus is a good idea.