The Alleged Date of Onset doesn't have to be either. You shouldn't choose a date until after you were working below the SGA level ($1040 per month).

If you were terminated because you could no longer physically perform THAT job, it could be a good date to go by. But remember, you can't perform any prior work or any type of work...

The documentation that your condition won't improve, and will keep you from working any job is what is key. If you are near ages 50 or 55, that might be considered as well, to determine if after that birthdate, would be a better alleged onset date.

I had to stop working due to an injury, and waited 2 years to file for SSDI. My alleged onset date was two years prior, and I received 12 months backpay prior the filing date. I lost six months or so by not filing earlier, but it would have been inappropriate for me to file earlier because I thought surgery would make me well enough to return to some type of work.

It sounds like you're participating in Voc Rehab? If so, I would wait until they test you and try and place you. If you can work, even with accommodations, you'll be better off. If they find you are unable to maintain any job above the SGA level, that will help provide documentation for SS.