I've emailed the image. Perhaps you can make out his place of birth from this image. I see that Juan/John Garza died 4/30/1970,last Soc.Sec.benefit was Los Angeles. Have you requested his Soc.Sec.application? He filled this out himself. It usually names parent's,including Mother's maiden name. Have you requested a copy of his death certificate? It's only as good as the information provided by the informant, but it may also provide clues about his parents.
I did find Juan and family in the 1920 El Paso Co.Tx.census.According to the information,Jessie immigrated to the US in 1904. She became a naturalized citizen in 1914.Three children in HH..Marie 4,Juan 2 and Lawerence 1.Juan was a hardware salesman.