It's not possible to give all new Air Force recruits the AFSC (job) they want, even if they're qualified. Each Air Force job has an assigned "manning level," which is broken down by rank. In other words, the Air Force constantly determines (for each job) how many first termers they need (Airman Basic through Senior Airman), how many Staff Sergeants the job needs, how many Technical Sergeants the job needs, and how many Master Sergeants the job needs.
At least once per year, the Air Force studies the manning-levels of each AFSC, and rates each AFSC (by rank) as "shortage," meaning there are not enough individuals doing that job in that rank, "average," which means the manning level for that job/rank is just right, and "overage," which means there are too many people in that rank doing that job. If the manning level for the first-term ranks (Airman Basic to Senior Airman) is projected to be "shortage," they issue "requirements" to the Air Education & Training Command (AETC), who in turns tries to make sure there are enough training seats, and -- in turn -- issues "slots" to the Air Force Recruiting Service. Job requirements for NCOs (those on their second or subsequent enlistment), are released for possible NCO voluntary and involuntary re-training (more on that, later).
Even if an Air Force job is listed as a "cronic shortage job," that doesn't necessarily mean the job will be open to a new recruit, even if qualified. Such factors as available training seats come into play. Or, the job may be "shortage" overall (because it has a shortage of NCOs), but may be adequately-manned when it comes to the first-termer ranks.
Additionally, some Air Force enlisted jobs simply aren't available to first-term enlistees. A couple of examples would be Equal Opportunity, or Education and Training, or Office of Special Investigations (OSI).
Air Force recruiters traditionally address these concerns by informing applicants who don't get one of their primary job-choices that re-training is possible after a few years of service. Enter the Air Force Re-Training Program.
The regulation which governs retraining for Air Force enlisted personnel is Air Force Instruction 36-2626 - AIRMAN RETRAINING PROGRAM.
The Air Force Enlisted Retraining program can be divided into three major areas: voluntary re-training for first-term airmen who have (amost) completed their first enlistment period, called CAREERS, (which stands for "Career Airman Reenlistment Reservation System"), NCO retraining (which applies to those on their second and subsequent enlistment period), and disqualified airman retraining (which applies to both first-termers and those on subsequent enlistments).
First-Term Airman Voluntary Retraining
A first-term airmen (four-year enlistment contact) assigned to a CONUS (stateside) base is eligible to volunteer to retrain after they have completed 35 months (no more than 43 months) of military service. A six-year enlistee (assigned to CONUS) may volunteer to re-train after completing 59 months of military service. For first-termers assigned to overseas bases, they may put their application in between the 15th and 9th month before their DEROS (Date Eligible to Return from Overseas Station), as long as they will have at least 35 months (four year enlistee) or 59 months (six-year enlistee) of service, at the time they depart the overseas station (in this way, approved applicants can be re-trained, en-route, before they report to their new duty station).
The only exception to the above requirements are for those volunteering to retrain into the Pararescue, Combat Controller career fields. Such individuals may apply for retraining after 33 months of service (four year enlistee) or 57 months of service (six year enlistee). This allows time for the individual to complete the Pararescue PAST or Combat Controller PAST, and required medical exams to include as part of their re-training application.
As an "exception to policy," volunteers for Pararescue, Combat Controller, SERE Instructor, any aircrew AFSC, and any linguist AFSC, may submit re-training applications after 24 months of service (four-year enlistee) or 36 months of service (six-year enlistee).
Those who are serving in the following jobs can volunteer to re-train into a "lateral specialty" after serving for 24 months (four year enlistee) or 36 months (six year enlistee): Security Forces, Physical Medicine, Aerospace Medical Services, Surgical Services, Diagnostic Imaging, and Optometry.
For example, a 3P0X1 - Security Forces troop could volunteer to re-train into 3P0X1A (Dog Handler) or 3P0X1B (Firing Range Instructor), after completing 24 months of service (four-year enlistee) or 36 months of service (six year enlistee).