It is not a race...and getting the application in early isn't going to make a weak application stronger.
That said, getting the application completed in a timely manner demonstrates organization, interest and motivation, so there is some benefit.
More importantly, Admissions isn't submitting your name to DODMERB until the application is complete (or nearly so in some cases), so getting it done promptly gives you time to address remedials, etc.
In other words I assume this means that earlier applicants are reviewed first, and therefore, have the most slots to compete for.
THis is incorrect. Yes, the early application might get reviewed by the Admissions Board first , but for most candidates, this is a two step process where the Admissions Board determines whether you are qualified, then Noms and Appointments has to determine who on the MOC slates is most qualified and gets the offer. Noms and Appointments can't do this until all Nominations are in, and Applications complete. That is why most Candidates won't know until Februrary and March, regardless of when you complete the application.
Bottom line, don't rush to be the first one done -- but submit the best application you can , in a timely manner, then be prepared to wait.... and wait...and wait. It is not just about a single candidate, but how that candidates stacks up against other candidates in their MOC pool. Yes, I have seen a candidates not even start his application until he received his nomination , interviewed last week of January, and accepted.
PS. I am reluctant to even mention this, because no one really knows what triggers and LOA or not, but the extraordinarially strong candidate might also get an LOA...but it appears to me that LOA's can get issues whenever.
Note, was typing this when Huursoldat posted...says essentially the same thing.