Before you start feeling anything, move your hands around. get in the habit of doing that all the way through the ride. The more weight your hands are supporting, the more discomfort you're going to feel. Your hands and wrists were not made to support your body.
move around the handlebar. ride with one hand, doing stretches with the other. This seems to be a permanent bicycle riding problem. Some people get aerobars. and there could be a fit problem exacerbating it. get fitted professionally?