If your Civil War veteran applied for a homestead under the United States Homestead Act, he would have to have proved his service. A copy of his discharge would in with the homestead application. If you’re having trouble locating his military or pension records, see what is in his homestead application first.
If there is not a “regular” civil record of your ancestor’s birth, determine if the office has a record of “delayed” births. These records were those created years after the actual event when it was realized the person had no birth record made at the time of their birth and they needed a copy of their birth record. Delayed birth records were usually made based upon the testimony of those alive at the time of the birth or documentation submitted from other records (ie. church records, government census records, etc.)
Applications for US military pensions often mention the act under which the veteran (or his widow) applied. The details of that act may explain why the veteran waited until then–and that reason could be a clue. Men or women who applied for federal property usually did so under a certain act. If you have records of your ancestor having “applied” for anything, look to see if the act under which the application was made is referenced. Learning about that act may tell you something about your ancestor that is not stated in the application.
If your ancestor naturalized, see what other people naturalized on the same day. If you found your ancestor’s declaration of intent, see who else made out declarations on that day. Look at the names of other people who got married on the same day as your ancestor. Are there clues in the other people who did certain things on the same day as your ancestor?