This is what keeps me up at night. I feel like I've been working on "break in" for 10 years. Experiences is a big factor. I've worked with a few self publishers and very small press magazines, but that was so many years ago, I am embarrassed to show my art from them to anyone. I shudder to think of using that as "experience" for an agent or editor.
But I think, I've realized, that for me, I've really have to work on the writing side. Good illustrators and writers are very in demand. And I think that having completed book dummies to show that you are capable of illustrating a story and completing a project is very important. They want to see that you can do the job.