Unix did not exist before 1970. Neither did tar. There are no tar files with files with timestamps before 1970 _unless_ you've used `touch -t 195001010000` or `utime(2)` or `futimes(3)` to set the files' time to before 1970. That seems pretty unlikely.
If I create a new archive format today and use it to archive the contents of my disk or whatever USB stick I find do you not thing it might end up containing files with timestamps before today?