Odds of Getting In
Here we have what is called a "conundrum." Assuming you have decided to take the "work experience" path, you need to hook up with a reputable aircraft maintenance shop so you can acquire the experience. However, in many cases, shop management won't consider you if you're not certified. Anyone up for a game of Catch-22?
Here's one possible option. Let's say you're close to a regional airport, or perhaps a general aviation airport that performs maintenance on privately owned aircraft. Perhaps the on-site maintenance shop would allow you to work as an apprentice, beginning as a gofer and floor sweeper. Can't you just feel that dirt under your fingernails?
Yes, you'll be bored out of your mind, but you'll work your way up the food chain as you build your skills. You'll work under a certified mechanic's supervision, and will eventually get to put your hands (and tools) on real live airplanes. Most importantly, you'll accrue verifiable work hours.
Talk to the Director of Maintenance—respectfully, of course—and be prepared to present your case. Don't expect to make much; in fact, some shops may not be prepared to pay you at all. Decide how much you want this career before you embark on this path. If the answer is "not much," we hear Lowe's is hiring.