Medicare Coverage Start Date?

For Disabled Individuals 

Medicare coverage begins 24 months after the Social Security disability benefits begin.

For all other individuals-those not disabled

Coverage start date depends on the date of birth if both of these apply:

• You sign up for Medicare Part A (Hospital Insurance) and/or Medicare Part B (Medical Insurance).
• You sign up during the first 3 months of your Initial Enrollment Period.

Ccoverage starts the first day of the month individual turn 65, unless the birthday is on the first day of the month. If the birthday is on the first day of the month, the coverage starts the first day of the prior month.

https://www.medicare.gov/sign-up-change-plans/getting-started-with-medicare