When you are awarded Social Security disability benefits, you do not receive benefits beginning on your onset date. Rather, there is a 5 month "waiting period" before benefits begin.
As a practical matter, however, it is often a 6 month waiting period. This is because the waiting period is 5 full months of disability. So if you have partial month, that month simply doesn't count. I have had clients with an onset date on the 2nd day of the month, and that whole first month did not count. So the effective waiting period can be as long as six months before benefits are due. The best possiblle onset date is the last day of the month.
For SSI benefits, there is no waiting period. Benefits accrue beginning the day you file for benefits.