I was a Navy officer years ago, so I will make some comments pertinent to officer promotions.
Neither. You don’t apply for promotion, nor do they care whether or not you are ready. For the first promotion from O-1 to O-2, promotion is automatic once you have the required time in grade (usually 2 years). All promotions after this are based on boards that meet and review the officer’s fitness reports (annual reviews) and their current and past assignments. The percentage of officers selected for promotion from O-2 to O-3 is also close to 100%, and officers are promoted to O-3 at the four year point for their total time in service. Selection percentages then go down the higher up you get, from ~80% selection rate from O-3 to O-4, to ~50% selection rate from O-5 to O-6. Getting selected for promotion to admiral is much more difficult. Senate confirmation is required for all promotions for O-4 and above.
After promotion to O-3, the promotion flow rate starts to vary, and you can get officers being selected for promotion “below zone” (i.e. early), “in zone” (right on time), and (rarely) “above zone” (late). Officers get two chances for promotion. If they are “passed over” for promotion, they get one more chance for a board to consider them for “above zone” promotion a year later. Officers who fail to get promoted after being considered by two boards are forced to separate or retire. (The latter is only an option for an officer with at least 20 years service.)