An extremely common and unfortunately ineffective strategy to break into the production side is to contact production houses cold, without ever having worked on professional sets, and offering to work for free. There are a ton of people doing this and I never hear of this getting someone connections or work.
One issue is that there isn’t a lot of overturn in editing. Once people are in those jobs they are locked in for the long haul, so you need a way to get inside and get referred.
You know where this is going: get inside a production assistant. Learn the set and the industry, make professional connections, and make your goals known. That conversation will happen naturally; you don’t need to force it. Professionals know you don’t want to be a PA forever, so the question of where you want to go in the industry will just pop up.
We’ve addressed editors, so what if you also want to write, produce, or direct? The pathway is going to be the same but you’ll be looking out for some specific connections and opportunities. You want to be working on your own stuff. Writing as much as you can, finding aspiring directors, DPs, and actors to work on personal projects with you as a writer, producer, or both.
You’ll build examples of your capabilities, and just like with editing, you’ll be networking toward people who can look at what you’ve made and eventually throw you bigger opportunities.
Everything in the film industry happens through referrals, especially the high level stuff. If you want to vector up into this big positions, you need to be getting connected!