This is a time line of how things went for my husband's disability. I hope it helps, we live in Cincinnati Ohio.
He was approved on April 1st, we got our 1st SSI backpayment in May and our 1st SSI payment around the 1st of June. Now they say they have his SSDI ready to begin next month (1st check on the 3rd of July) and that we should see our backpay on SSDI soon (we will no longer recieve the SSI,because that is only based on need, and with the SSDI, we will not need that)
I hope this helps you, I would estimate you should recieve SSI this month, at some point. Have they took your bank info to recieve direct deposit yet? If they have check your account often. The SSI is a small amount each month (at least in our case) until you recieve your benefits from SSDI,which will be a larger,more significant amount. Good Luck! -Rachel