Setting the first word, first few words, first phrase or sentence, or the complete first line of each chapter in small caps, sometimes preceded by an initial or drop cap, is done by the typesetter in the course of the interior design of the book. It is never a part of the author's manuscript, unless, for example in scientific essay collections, the publisher explicitly asks for publication-ready, styled manuscripts and provides a style guide.
Practices regarding this vary with publisher, type of book, and/or book designer. There is no rule how this should be done, though there are style guides, like the Yale University SEAS Monograph Styles, that request: "First few words of each chapter: in small caps" (p. 3). Here is a relevant discussion among typographers. And here a book designer explains the use of drop caps and recommends:
You can also add to the effect you’re creating at the beginning of the chapter by emphasizing the first few words following the drop cap. You’ll see this done with small caps, often with some letter spacing. To use this approach, decide on a standard number of words between 3 and 5 and keep all the chapter openings consistent.
Other common ways to emphasize the first few words after a drop cap (or without one) are italics and bold text.
I see the first few words in small caps often. I read a lot of SF&F pocket paperbacks, and it is quite common with some publishers.
Don't do this in the manuscripts that you send in to a publisher!!! Always follow the manuscript guides, usually published on their websites.