I can finally answer the question based on experience.
According to SSA I applied in September 2011 although the judge concluded I was actually disabled from 2008. I had a hearing with that judge in spring of this year... sorry but I'm not good with dates... so lets say March 2014. I got a letter of fully favorable decision last week. I got a notice of award letter yesterday. I will get a small monthly payment beginning in late August. I'll let you do the math but the amount of time between filing date and receiving an SSDI payment looks like 3 years to me