Hoods have been attached to shirts for centuries. Take Robin Hood, for one. (What is it with all these recent Robin-Hood-adjacent profiles?) He wore a hood, right? (At least Kevin Costner wore one on screen...) Then you have medieval monks, always pictured in hooded cloaks.
But that's hoods, and here we're talking about hoodies. If one defines a hoodie as a hooded sweatshirt (and NOT a hooded cloak), then it all goes back to the Knickerbocker Knitting Company. It was started by the Feinbloom brothers in 1919 in Rochester, New York. In the 1930s, the brothers got the idea to add a hood to a sweater (Rochester is blisteringly freezing in the winter), and the modern hoodie was born.
The company was renamed to Champion Knitting Mills, then just shortened to Champion. It's still known as that today, and is still a leading producer of hoodies. The brothers are long gone, of course, and the company was purchased by the then-Sara Lee Corporation in 1989. (What is it with all these recent Sara-Lee-adjacent profiles?)
Jews might not have invented hoods, but they definitely invented hoodies! (What is it with all these recent fashion-adjacent profiles?)