Dates on coins didn't appear routinely until the late 1500's.
Here's an example of just such an undated thaler:

There are die variations between this coin and yours, but that's normal enough for this series. This coin is in the name of
Archduke Ferdinand II of Tyrol (1564-1595), son of Emperor Ferdinand I (1521-1564).
The Davenport catalogue of world crowns and thalers has this footnote on these coins:
The coins of Ferdinand are rather common. In fact all the various [1 thaler coins] are simply varieties of other [with one or two notable exceptions]. Please note that "common" is a relative term! They catalogued at $275 in EF back in 1981! The linked one above sold for $710 against a $1000 estimate at the Triton X sale a few weeks ago.
There are seven varieties of undated Ferdinand thaler listed in Davenport for the Hall mint alone. And not one comparative picture or guide to assist in distinguishing them. Not that it really matters; CV for them all is the same.
If it is a fake, then it's most likely a fake of a real coin, and not a spectacularly rare one at that.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis