All were hammered in those days. TBH I am unable to identify the date on the dinar but ANACS has specific dates on all 6 dinars they graded for me. I am assuming it is somewhere in the text and probably stated as year of reign.
I have several older coins, but my oldest dated coin was produced in 356/5 BC. The upside-down crescent-shaped stroke above the reverse galley is the symbol for 10, which signifies the 10th regnal year of Abd'ashtart I. Phoenicia, Sidon. Rev.: Galley to left on waves; date (curved hash-mark) above = 356/5 B.C. Obv.: Persian king or hero in kneeling-running stance, right, holding spear & bow. Weight: 3.32 gr. Diam. 14 mm. Attrib.: Hoover Vol. 10, Pg. 71, #251 (Year 10).
Yes, the designers/engravers of ancient Tyrian coinage utilized dating on several issues. Here's another early dated coin only slightly less old than my Sidonian above. This little Tyrian silver obol was issued just a few years after Alexander the Great rolled through and began producing the nearly ubiquitous (in that day) Alexander/Zeus types. The date appears in Phoenician numerals, signifying 21, which dates it to 329/8 B.C., over 23 centuries ago! (See the red squares for date location.) Sorry for the small, low quality images. BTW: The type is Price 3253.