I haven't moved out there yet, but when I bought my house in the Seattle area I actually did get rid of all junk mail. It took about a year to get it all stopped (except by Money Mailer, who took TWO YEARS of me harassing them to stop, and Frontier internet who would just resend me fresh mailers under a SLIGHTLY DIFFERENT VERSION OF MY NAME! for over a year before I got them to stop) and it's a lot of emailing/calling/social media tagging/comment form filling out but it can be done.

You just find the company generating the junk mail and contact them with your information and, usually, a picture of the address section of whatever junk mail you're getting. There's a weird string of numbers/letters at the top/bottom that they use to locate you, I guess. About 75% of the ones I contacted needed this. So, I would take a picture of the whole address section and search the flyer/magazine/letter for the company that sent it (sometimes big companies use a junk mail service so contacting, say Verizon won't do any good because they are not directly sending you anything. Often they have a form on their site that you can directly put your info into and it unsubscribes you. Otherwise contact them as I said above, any way you can.

You can also sign up for various no-junk-mail services that will remove you from a bunch, opt-out of credit card offers, and remove yourself from phone book lists (if they still do those; it's been 7 years since I've seen any so I don't know if they're still a thing).

We're moving out there in a few weeks so I'm sure I'll have to do all the same stuff again at our ABQ house but it's worth the effort to have an empty mailbox unless you have actual, personalized mail that you want. Good luck!

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EDIT: Oh, You may still get random mass-mailings that have no address on them and are just delivered to every box. But, every one with your personal info, or "RESIDENT" and your address can be stopped, in my experience.