A 'baby essential' today: the comfort blanket, soother, or cuddle blanket. It will most likely be baby's favorite plaything, often going everywhere with them. You'll probably struggle to get this one in the wash, unless you can make several and swap them out. You could try making different types - a quiet snuggle version, and a more active play version with crinkle lining.
I have made some of these little cuddle blankies. Thanks for the hint to add crinkle lining for fun.