You must send a trascript matching form with your transcript and that form is only available once you have started your application for that cycle. So the earliest you could send it is June 3rd (if your registrar's office is super fast at processing and shipping).
FROM ADEA: "1. Arrange for a sealed official transcript, accompanied by a Transcript Matching Form to be sent directly to the AADSAS Transcript Processing Department from every accredited U.S. and Canadian institution you have attended. AADSAS [FONT=Arial,Arial][FONT=Arial,Arial]will not..[FONT=ZWAdobeF,ZWAdobeF][FONT=ZWAdobeF,ZWAdobeF] ..accept student-issued transcripts or transcripts sent by an applicant. "