For the pastry crust, whisk together the almond flour, coconut flour, tapioca flour, oat fiber, and salt in a large bowl. Cut in the butter and cream cheese until it looks like coarse crumbs. Whisk together the egg and vinegar, and add it to the almond flour mixture; mix with a fork until it forms a dough, lightly kneading it together with your hands a few times if necessary. Form the dough into a ball and then flatten it slightly into a disk; wrap in plastic wrap and chill (about 10 minutes in the freezer or 1 hour in the fridge).
For the filling, heat a medium skillet over medium heat. Once hot, add the butter and once melted, add the mushrooms. Cook until they’re starting to brown, about 10 to 12 minutes, stirring occasionally. Add the garlic, thyme, salt, and pepper, and cook 1 minute, stirring constantly. Cool to room temperature.
When the pastry dough is chilled and the filling is cooled to room temperature, preheat the oven to 350F and line a large baking sheet with parchment paper or a silpat liner.
Divide the dough into 6 equal pieces; roll each piece into a ball, and then roll each ball between 2 pieces of parchment paper out to a 5 to 6-inch circle. Divide the cheese between the 5 pastry circles, and top with the mushroom mixture. Carefully fold the outer 1 inch of the dough up over the filling.
Arrange the galettes on the prepared baking sheet and bake until the pastry crust is golden, about 25 minutes.