The only easy way to attain AA status is to have it gifted to you, either by the company or by another elite. Still, there are some avenues to shorten the climb.
AA Elite Awards allow Executive Platinum members who earn 125,000 EQMs to gift AAdvantage Gold status to a friend for one year.
A company enrolled in Business ExtrAA can redeem 2,400 points (equivalent to $24,000 in spending) to give Gold status to an employee.
AA does not generally status match except some cases negotiated through corporate travel departments; however, earlier this year they pounced on problems at United to poach some upper tier Premiers with matches.
Citi Executive AAdvantage World Elite MasterCard — Each calendar year when you reach $40,000 in spending on purchases, you will earn 10,000 EQMs. This card is also sometimes promoted with a one-time signup bonus of 5,000 EQMs for new cardholders.
Completing a challenge is usually the easiest way to attain status quickly if you have travel already scheduled, particularly if in a premium cabin as the challenge is based on EQPs, not EQMs. Note that the challenge is only offered to attain a status, not to maintain it.
AA periodically runs double EQM promotions.
If you're a true mover-and-shaker, someone who is giving AA hundreds of thousands of dollars of business over the years in full fares, you may be invited to the Concierge Key program.
Also, while the AAirpass prepaid card no longer comes with status, it does come with Admirals Club membership and priority checkin/screening/boarding.