You can sign up for free Part A (if you’re eligible) any time during or after your Initial Enrollment Period starts. If you sign up within 6 months of your 65th birthday, your coverage will start the first day of the month you turn 65, or the month before you turn 65 (if your birthday is the first of the month).After that, you’re coverage start date will go back (retroactively) 6 months from when you sign up. Example.Mr. Green's 65th birthday is July 20, 2016. If he signs up for Medicare in April, May, or June, his coverage will start on July 1, 2016.fter that, you’re coverage start date will go back (retroactively) 6 months from when you sign up. Example. Mr. Green's 65th birthday is July 20, 2016. If he signs up for Medicare in April, May, or June, his coverage will start on July 1, 2016.