In this business, it's not what you know but WHO you know... and who THEY know... and who THEY know... and so on and so forth. Just start asking friends and family if they know anybody out in Los Angeles or New York or if they know somebody in television and film. Hit the pavement, kids!
Secondly, trying to get a meeting with a production company without an agent is difficult. It has been done before, but more out of luck than anything the film makers actually did. Go for it! Be creative. But, my only caveat: Hope for the best, prepare yourself for the worst.