Iso Birth Sibling Aug 1985-may 1986 Austin, Tx Lutheran Social Services Of The South

I'm searching for my birth sibling that was adopted at birth between Aug. 1985 and May 1986. I do not have the exact date of birth. The birth and adoption took place in Austin, TX. The agency that was used was Lutheran Social Services of the South in Austin, TX. Does anyone have any advice on how I can search without the date of birth? The agency will not provide me any non-identifying information since I'm a sibling.