Although the word “jigsaw” didn’t exist before the jig saw was invented in the late Victorian age, such puzzles did exist, cut out with marquetry saws. They were called “dissected maps.” Apparently, puzzles go back to the 1700’s, when they were primarily maps cut along the borders of the countries/counties, etc. You can see an example of two on my Pinterest page. I even saw them mentioned in a period account as a popular gift for loved ones on Valentine’s Day!