What a bugaboo. You can't get hired without it, and you can't get it till you're hired. The answer is to sell not your experience, but your abilities. That means learning all you can about the job you want and figuring out for yourself how you'd apply your abilities to doing it. Every job involves a learning curve.
Smart managers hire people because they can ride a fast learning curve.
Prove you're one of them. Be ready to demonstrate to an employer that you've done your homework, you know what the work entails, and how you're going to apply yourself to it. This will take a lot of research and talking to people who do the work you want to do. They're also the people who will introduce you to the right managers. In other words, forget about job postings, want ads and resumes.