Place the berries in a medium saucepan. Using a potato masher, lightly mash the berries. Add the maple syrup, lemon juice, orange juice, and thyme. Bring the mixture to a simmer and cook, stirring occasionally, until thick, 50 to 55 minutes. Cool to room temperature, about 1 1/2 hours (the jam will continue to thicken as it cools). Refrigerate in an air-tight container for up to 1 month.