I've recently lost my job, and I'm working towards changing vocations. My degrees are in Mathematics, but I'm interested in IT, particularly working as a DBA or a programmer.

I don't have IT experience, but I have the resourses to be patient with the transition, and I'm currently learning SQL and Java.

Obviously, I need some job experience. My question is this: What entry-level jobs might allow me to gain useful experience towards obtaining a DBA job?

It seems to me that programmers often start as testers, and system administrators could start at a help-desk position, but it is unclear how one begins to work with a company's database.