I think you are mixed up about a few things.

SSI is only given to disabled persons who either don't get any SSDI, or whose SSDI is very small. The maximum SSI benefit is now $733. That's the amount the federal government would give you, if you were found disabled and weren't getting any SSDI, due to not having worked long enough. (Some states kick in a bit more money to their residents who get SSI.) For people who do get SSDI - but only get a small amount (meaning less than $733) - the federal government will grant you SSI in an amount to bring your total up to $733.) So if your SSDI check is $733, or more, you won't get any SSI. (In some states, you might get a small amount from your state.)

The other thing you are confused about concerns the Social Security Administration holding back payments for an interval. That interval is 5 months, and it is counted from the first day of the onset of your disability. Then, when your checks start, they come a month after they are earned. So the waiting period ends up being 6 months after the start of your disability. That applies equally to both SSDI and SSI.

You can ask your attorney what date he is using as the onset of your being unable to work. That date was put on your application for disability. It might be the same as the date you applied, or it might be earlier.

If you haven't done so yet, be sure and apply to your local housing authority for a federal housing subsidy (Section 8 Subsidy.) There is a long wait to get that (a few years,) but it can add a few hundred dollars a month to your income.

Also, apply for food stamps now, if you haven't already. You might get those immediately.