You can start working on your personal statement at any time - I think that's usually where most people procrastinate (not to mention it takes a long time to revise and rework something to an acceptable level of quality for submission).
Also, as soon as you get grades for your spring semester courses, request transcripts from all the schools you've attended - in addition to the transcripts you will send to AMCAS - just for your personal use. When you fill out the course information on the AMCAS application, you'll need to know the course name, number, and the grade you received. (So having a personal copy of all your transcripts helps immensely.) Also, be sure that you have your school(s) send your transcript to AMCAS as soon as possible. Sometimes it takes a while to have transcripts sent.
You can also begin to compile a list of your extracurricular activities, honors/awards, publications, relevant medical experience, leadership positions, etc. There is a section on the AMCAS app. for about fifteen of these "Postsecondary Experiences" you've had, and you're expected to write a short description of each activity/honor. This section is important in showcasing yourself to the adcoms.
Getting everything in early means submitting your AMCAS in June or July. It takes AMCAS quite a while to verify and process your app, so the earlier you submit it, the better. You don't even have to wait for your MCAT scores (although I also recommend that you take the April MCAT!)