I'm not sure how it goes with SSI, but with SSDI what actually happens is you will get back pay dating all the way back to the first day you were deemed unable to work.
You may get too sick to work and not file for 6 months or maybe longer. Then, it might take up to 2 years to get approved (that happened to me). When you are finally approved, you will get a lump sum payment for that entire time.
That lump sum will arrive in the form of a single check in a matter of only 2-3 weeks and then your regularly scheduled monthly checks start coming after that.
Lemme tell you, it's a happy day when you are FINALLY awarded what you deserved since day one...