Well, it depends on what you mean by “perfect mint condition.”
I have this coin (1712) in an NGC MS61 slab: N#33781
I have this coin (1689) in an NGC MS61 slab: N#87663
I've got a couple of raw coins from the mid-1500s that I am confident would grade at an MS level with NGC, like this one:


This Polish-Lithuanian type is on the market in very high grades even back to the decade of the 1510s.
If you mean something like MS65, then yes, it is less likely we have a member with a coin at that grade from the 16th century.