Yes, you can branch Med Service (MS) and compete for a 67J position directly out of West Point. General process for West Point is you will preference and branch MS while making sure to complete the normal flight qualification process to be eligible. The flight physical process begins junior year with you taking the SIFT and beginning your flight physical. Following successfully branching MS and assuming you came out with passing SIFT (not hard, wouldn't sweat this part) and a good flight physical (harder for some, particularly if eye surgery is involved. start this process early), you then will interview and compete for a 67J position with a branch representative at the Academy. You'll be notified before graduation if you were picked up. If you were, you'll attend flight school after attending MS BOLC after graduation. If you weren't, you'll be a regular MS officer.
Big Army, if you are a MS officer but not flight, you can apply within the branch (SIFT, flight physical, formal application, interview, etc.). This can occur all the way up until about CCC. If you get picked up as a LT/junior CPT, you'll attend flight school and whatever appropriate PME you need for your rank before heading to a MEDEVAC unit.
MEDEVAC is an extremely small community as you've already noted which makes competing for these slots competitive. Things to note, if you branch MS out of USMA and do not get the 67J designator, you'll be serving as a regular MS officer. Think a lot of hospital administration work. Very important; very much not flying. MS is also historically competitive branch to get out of West Point even before you look at the population competing for the 67J slots within it. You'll need to do well to have a good shot at even getting to the point of being able to interview for the job.
Pros: 67J's actually spend a disproportionate amount of their company grade time actually at the company compared to a 15A (normal AV officer) because of the way that a MEDEVAC company is set up (O4s are COs, O3 are PLs, LTs serve as section leaders) which allows them sometimes to build flight hours faster than their 15A peers. The BOLC/CCC tends to be extremely lax compared to other branches. Downside: you're only doing one type of flying with no crossing over to any other kind of aviation unit. 15 series officers serve in MEDEVAC communities when there's a shortfall of 67Js so they can receive the same experience with the mission set if they are UH60 pilots. Your WO's will bounce back and forth between mission sets (they are all AV branched).
