tar files are not guaranteed to have any kind of "archive header". GNU tar has an optional "volume header", used to help identify the members and sequence of multi-volume¹ archives. Other versions of tar might not have this feature. Of course, if a tar file does have a volume header, its mtime would be the creation date of the archive, so one could stop reading the file once the volume header is read.

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¹ "multi-volume" means the tar file may not be the complete archive. The archive may been created in size limited chunks. Use of this feature makes the individual tar files usefully extractable (as opposed to splitting a single tar file, which would require re-assmbly, first). Of course, a file that crosses volume boundries can only be partially extracted.