For the thumbprint cookies: Preheat oven to 325 degrees F. Line a cookie sheet with parchment paper.
Cream butter and pudding mix together in a large bowl until light and fluffy, then beat in the egg. Add the flour and salt, beating at low speed until a dough forms.
Put granulated sugar on a plate. Roll the batter into 1-inch balls, then roll through the sugar and place on the lined cookie sheet. Make a thumbprint in the center of each.
Bake until firm to the touch, 15 to 18 minutes. Transfer cookies to a cooling rack immediately and let cool completely.
Fill each thumbprint with the preserves.
For the cream soda glaze: Whisk together powdered sugar with the cream soda in a small bowl until smooth, white and shiny. Drizzle glaze criss-crosses over the cookies and let dry completely, about 20 minutes.