First-novel writers need to have a novel in hand before approaching publishers. Sample chapter plus outline works for people who have already had novels published, but there are too many people who can’t finish a book for a publisher to make any kind of deal with a first-timer unless there’s an actual concrete book on paper for them to evaluate.
Write the novel, then pick the most likely publisher, write a cover letter, and send the book. Be prepared to wait up to a year for an answer. Have 3 or 4 follow-up publishers that you can send it to when it comes back; be prepared to wait up to a year from each of them. (None of them will accept simultaneous submissions, and if two of them accept it and you have to tell one you had it submitted at multiple places, you’ve just blackballed yourself out of publishing.) If you get a publisher who’s interested, then you contact an agent to negotiate for you.
Until the book is written, there’s no point in contacting a publisher.
Until you have an acceptance, there’s no point in contacting an agent.