This is a medal, not a coin. The difference is important because it explains the intricate detail you see. Medal-making was innovated in the Italian penninsula in the mid-late 15th century: a process of fine casting in bronze, among other metals. These casts could then be refined through engraving and polishing. They maintain their level of relief and detail because they were not handled like currency.

In this case, your medal of Mehmed the Conqueror was made by a student of the renaissance sculptor Donatello, Bertoldo di Giovanni.

Notwithstanding the above, coins were struck by hammer and hand until the mid 16th century using two-part iron & steel dies. The 16th century saw the development of drop presses, screw-presses and striking and lamination combination dies. By the late 17th century 'automation' as we might recognize it today (screw press and fly press) was fitted into mills to produce coins at scale.