I only know of one person who went straight from college to a full-time DBA and he spent about 18 months as an unpaid intern first. Since you have zero experience, the best place to start is at the help-desk at a large organization. Other than that... look around, talk to people, network like mad. You might find someone willing to take a chance.

Get a copy of Tom LaRock's book DBA Survivor. It might help some.