Please note this is exactly what i did and 1-3 days later i received my code, so it's probaly not a coinidence(sic)
1. Login to EA of your account
2. Add the games of battlefield series (i added BF2, BF1942)
3. Add BF3! i did this because it was there
4. Explore around the Origin Site (i did this but dont know if it's related)
when i did this, within 3 days i got my invite... i think the age of the account, the games you bought over the years and what your interests/jobs are (if in IT i think they think that you understand tech stuff) is part of the invite process
this is what i did, you can try too so dont get angry if it doesn't work.
Please note i only have added Battlefield games on my EA account so i don't know if this also makes a difference.
P.S i don't think it's against the rules to post when i did which MAY get your an invite.
Disclaimer: Please do not use any of this information, I do not condone any use of this informtion, it's for educational purposes only.