The soonest you can begin filling out the FAFSA for the next school year is October 1. The deadline is June 30. So if you are a senior in college and know you want to attend graduate school, you could fill out the FAFSA as soon as October for attendance in a graduate program the following fall. The last day to submit the FAFSA would be the June 30 that falls after the October 1st starting date.