How can I gain an edge over candidates that are more qualified than me?

It's important to remember that there is much more to landing a job than your qualifications. You have to fit in to the work environment, and you have to be useful. Do your homework. Through your research and understanding of the job, you can show that you are more interested than people who rely on their qualifications. You can show that you are more motivated and more able to work without guidance. In short, prove that you are the best fit because you are not only able to do the work, you will do the work before it gets assigned to you. You may be the construction executive they expect least to hire when you walk in. That's fine as long as you are the one they remember most when you walk out.