This is straight off the Academy website:
The USNA uses a selection process known as "rolling admissions." As soon as all of your candidate packet forms are received, the Admissions Boards will determine your scholastic "whole person" qualification. If your record of achievement is truly outstanding, you could receive an early offer called a Letter of Assurance. This indicates our intent to extend an Offer of Appointment, provided all your remaining requirements (nomination, CFA, Blue and Gold Officer interview and medical) are successfully completed. A Letter of Assurance could be received as early as September of your senior year. Of course, final admission will depend on continued success and good standing in your high school as well as continuing to maintain your qualifications for the Naval Academy.
If you are found scholastically qualified but do not receive a Letter of Assurance, you will be competing for an Offer of Appointment from within your nominating sources. Approximately 3,000 candidates are found fully qualified (scholastic, medical, CFA, and have obtained a nomination) each year. Of that number, about 1,400 will receive appointments and approximately 1,200 become midshipmen. Most candidates will be notified of their final status by April 15.
All appointees should notify the Admissions Office of their intention to accept or decline by May 1. Except in very unusual circumstances, candidate files not completed by January 31 will not receive further consideration.
Notice that it does NOT say "get your application in early and get appointed early". Believe exactly what it says: Most candidates will be notified of their final status by April 15. Notice the word "by" and it's definition. Notice that it is in bold letters. Don't make things up in your mind. An appointment cannot be offered until a nomination is received and the deadline for Members of Congress is Jan 31 right along with the candidate's deadline. So the majority of action happens after that date. All the term "rolling admissions" means that admission appointments do not go out all on one day. If they did it would probably be on 15 April anyway.
The only thing that the Admissions Board can do is offer an LOA and, again, reading the above those only go to a "truly outstanding" candidate and not just every candidate that looks good. And those candidates still have to get all the other boxes checked on their application including a nomination. Sure, there are some candidates who seem to beat the crowd and are appointed "early" but their nomination may have come from a Congressperson who has early interviews, the Sec of the Navy, the President, the Supe, the VP and all the rest of the stray cats and dogs other than the usual member of congress who does the interviews right before Xmas.
Where getting your application in early, let's say August, is advantageous is that the Admissions Board in September has a bit more time to mull over a candidate before giving a thumbs up or down. The workload is lighter and they don't have a deadline staring them down. And if you think about it, that is exactly what a candidate wants----time for the Board to really look at their application and discuss it before making a decision. Take that same application and put it in right at the Jan 31 deadline and the Board that sees it is dealing with a literal tidal wave of applications and their now their deadlines are as real as a heart attack.
The modern concept of instant gratification is not a foundation of any military I know of.