Google’s answer would be to buy Ads — and increasingly that’s my answer as well. But in terms of organic techniques, there are a couple of tactics that might work.
The first is that you need to have content on your website that showcases your services in the area where you lack a physical location. The best way to achieve this typically is a case studies section with a unique page for each major market (or neighborhood, depending on the density of customers) that you serve. Before-and-after photos, videos of your staff at the job site, and testimonials from the customers you’ve serviced are an engaging and effective way to build content that shows Google you really do operate in these markets.
The second is a little more difficult to execute on but relates to reviews. “Number of reviews with City” was the #3 individual ranking factor in Local SEO Guide’s 2017 study. So if significant number of your reviews of your nearby physical location contain the name of the city in which you actually performed the service, there’s a reasonable chance that location would rank in a local pack in the adjacent market. You can’t force your customers to use any certain phrase in a review, but you might be able to prime your customers’ instincts about what to write about by first asking “where did we perform the service,” for example, prior to your review request.