You are correct, Cards were not issued until 1936.
Dear Ms. Strickland,
Thank you for posting your request on History Hub!
We searched the U.S., Social Security Applications and Claims Index, 1936-2007 on Ancestry and located 626 entries for persons that, according to Ancestry, passed away in 1930. Based on the examples we found, these appear to be entries for survivors claiming death benefits, rather than applications for a new card.
The National Archives and Records Administration does not have custody of these records. Genealogical websites that publish these records acquired them directly from the Social Security Administration. Please contact the website where you found the information and the Social Security Administration for questions about these records.
We hope this is helpful. Best of luck with your family research!