Searching for work...

I've come to a crossroads, perhaps even a cul de sac.  I've been trying to pull information on publishers to submit artwork, in an attempt to find work.  I've found that most publishers don't even accept unsolicited illustrations or manuscript(children's books seem to be an exception).  A few sites such as Houghton Mifflin Harcourt http://www.hmhco.com/faq.html#submissions_manuscript suggest to contact literary agents.  OK sweet, but still there is a problem.  Agencies normally don't accept anyone until they have a few years of work experience in the field!  So what is going on here?  Why does this continue to play like the chicken and the egg?