Most jobs aren't what you know, they're who you know. That's how you get a leg in the door. Even when you're establishing a career and places tell you that they're not hiring. Ask for an informational interview with a manager or department head for the area you'd like to work in. Ask them questions like "what do you look for in candidates?" "What is the most challenging aspect of working in this field?" "What are key traits that help you excel in this role?" They may not be hiring right then, but it opens up the door to make a connection, it show's you're a go-getter and it will likely cause them to remember you down the road whenever they are looking for someone.