As noted above, there are exceptions but in most cases I would think you will not have a competitive application until you have had a chance to prove yourself in the fleet (so probably 6 months after finishing all schooling).
The reason for this is that you need to have your command's endorsement for OCS. Company and Bn. Commanders for MCT or follow on schools generally do not get to know their students on a personal basis and cannot offer a constructive recommendation on a Marine's potential as an officer. Again, there are exceptions, but more commonly you will need to be in the FMF to be a serious candidate.
Good luck. These days enlisting is not the worst way to apply.