How to make coffee that closely resembles early 16-17th century coffees?
I can't answer for the 17th century, but Townsend's has a nice (but long) video on how they prepared coffee in 18th century America.  That'll bring you closer to the year you're looking for.

Also, note that, in Europe at least, imitation coffee was quite common. Both deliberate imitation, and fraudlent sales of not-really-coffee.