AACOMAS doesn't open until June 1st. All that anyone can do at this point is fill out the application and send in transcripts/LORs. It is definitely considered applying early if you're ready to submit by early June.
Applying early means that you generally speaking, submit before mid to late July. AACOMAS opened at the begining of May, you will be able to send that application to schools June 1st. What people do after May 1st is fill out the application, get transcripts and MCAT scores sent in, and wait for AACOMAS to verify your transcripts (which can take quite some time in some occasions).