Dear Ms. Rucker,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located the Population Schedules for the 1900 Census in the Records of the Bureau of the Census (Record Group 29). While some schedules are available online through the National Archives Catalog, the ones for Union County, North Carolina are not yet uploaded. Therefore we searched the website of our digitization partner Ancestry and located the listing for George Middleton you reference. George Middleton’s place of birth is given as North Carolina.
Before 1913, no births were recorded in the state of North Carolina by counties or states [exceptions are the cities of Raleigh (births begin 1890) and Wilmington (births begin 1904)]. After the introduction of birth certificates in North Carolina, some persons applied for delayed birth certificates that are kept by each county's Register of Deeds. Since it was not mandatory, there will not be a record for all persons.
You may wish to review the Genealogy Research web page of the State Library of North Carolina and the North Carolina, United States Genealogy page of the FamilySearch Wiki for more information about researching persons from North Carolina.
We hope this information is helpful. Best of luck with your research!