Have you checked the Ellis Island Immigration records?There is a Julio Aldana who arrived in New York in the year 1924 at age 28.Does this sound like it could be your grandfather?If so, that could be a start for going back to other ancestors.
I don't share your last name, but I do share a similar history on my paternal grandfather's side. He fled to the U.S.(as a stowaway)probably in the late 1800s or very early 1900s from Guatemala to New Orleans.There was mention of a decapitation while he was fleeing or on the boat (that may have been common at that time). His mother (we don't know her name, supposedly came from Barcelona).It has always been a mystery to me as to why they were in Guatemala.I concluded it was probably due to civil or political problems in Spain.His fleeing from Guatemala to New Orleans, we were told, was due to a military or political issue.He came to the U.S. in refined clothing and was educated.We suspected he must have come from at least a middleclass family. Like you, I wish I knew my family history.