Again, some great advice from just about everyone here, but pay attention to Mr. Wilkins. He's given the best advice that I read here. Right now, the best things for you to do are these:
1) Get yourself (and your reputation) established quickly. The first and foremost way to do this is to do your job, and to do it well. If it takes extra hours, then so be it. That makes you stand out. Collateral duties, volunteer work, and LOC's don't mean much if you're not doing the primary duty that the Navy is paying you to do. If you finish your PMS early or quickly, go help someone else with theirs. DO EXTRA WORK!!!! If you're doing your job in a manner above and beyond what's expected, trust me, you'll get noticed. And if you're too new to know how to do any of the extra work, then get yours done, and then go learn how to do the other stuff. Ask questions. Get a reputation for being someone who WANTS to learn all he can. Once you get your primary job stuff taken under control, heed Wilkins' advice and go volunteer for a collateral duty. I don't know much about "airdale" c.d.'s, but ask your LPO to task you with one. And even though Wilkins suggested you go to your Admin Dept., I suggest you stick to c.d.'s within your division, or perhaps your dept. at first. Like I said, your primary duties are first and foremost to your own division and dept, not the command. However, a departmental c.d. would be nice, too. Again, work hard to do it right. Even if it's a relatively low profile c.d., a job done well will get you noticed, and they'll soon task you with more responsibility. All that extra stuff recommended (college courses, volunteer activities, etc.) are nice, but don't mean much (from your chain of command's perspective) if you're not doing your job well. And like Wilkins said, QUALS, QUALS, QUALS!!!!!
2) DO NOT go outside of your chain of command. Like previously mentioned, get your ducks in a row, and submit a chit through your coc. Your ducks include #1 above, your previous LOC's (the ones you mention in your profile bio), your SAT/ACT scores, LOR's from your last CO, and even a note from your Chief and DivO. Include all these things with your chit. Few young sailors know that you can submit "attachments" with request chits, but if they will help your case, then by all means, include them. You can even include a personal statement pleading your case as to why you should be allowed to apply. And like previously mentioned, your CO is the ONLY person who can bottom line it "NO." Going outside your coc by going straight to the CMC or anyone else will definitely earn you some bilge-scum points. You don't want these.
3) After you get 2 & 3 taken care of, then concentrate on everything else, like college/PACE classes, volunteer activites, extra-curricular (non-Navy) stuff. The stuff in 2 & 3 are most likely the only things that will have much impact on the final decision to let you even apply or not.
Trust me, this is experience speaking.
I have seen policies like this before, and Wilkins is right--this is often something formulated by the CCC in absentia of a formal CO's policy on the matter. However, even if it is the CO's policy, these things often aren't written in stone, and are always up to the CO's discretion. So if you QUICKLY prove yourself as a high quality AME with alot of potential (by concentrating on the things in #1), then the CO may recognize your potential and give you a shot. So don't get discouraged by what your CCC told you.
And then there's this: there's always next year. I know it sounds cliche, but you're young and so is your Naval career. I've read your bio and some of your posts, and you certainly seem like a competitive candidate. So if you don't make it this year, follow the advice here, and you'll be a VERY strong competitor next year. Again, trust me on this.
GOOD LUCK!