Spray the brim of your baseball cap with a water bottle and begin to slightly bend the brim. The brim needs to be only moist, because a soaking wet bill can shrink.
Place a large softball underneath the brim of the baseball cap and bend the brim a little more to conform around the softball.
Wrap rubber bands around the brim of the cap to hold the softball in place. Place rubber bands on the front, middle and rear of the brim so it bends in multiple spots to shape around the softball.
Let the cap sit this way for a day or two before removing the rubber bands. Try on the cap to decide if you need the brim bent even more, or if this method has worked to your satisfaction.
Repeat as needed. With a newer hat, you may want to wrap the brim around the softball with rubber bands on a regular basis. The brims on newer hats may slowly flatten if you're wearing it throughout the day.