You absolutely don't need to handwash the dish first when using a modern dishwasher. You just need to scrape off large scraps into the trash.

I lightly rinse the worst dishes while loading until the water gets really hot at the sink next to the dishwasher. Having that prewash be very hot does a lot to make sure it gets it good in my experience.

US dishwashers tend to assume the incoming water is from the hot water line and is pretty hot. It takes a bit for the tub to actually get the water very hot, so you'll end up spending most of the pre-wash step with only mildly warm water if you don't get the hot water there first.