Process CSV files that follow the first nonempty one
If we reformulate this as trying to extract the header + body of the first non-empty file and the body of all subsequent files this comes to mind:

aggregated_file = ''
for file in list_of_files:
    if aggregated_file:
        aggregated_file += extract_body(file)
    else:
        aggregated_file += extract_header_and_body(file)