You would start with foam, then do something that coated it. Maybe a vinyl wrap, like they do with cars?
There are also plenty of ways to actually seal foam so it looks glossy and smooth. May not be something you'd be 100% willing to do, but I'm sure you could find someone you could hire. Here's a quick result from google on "how to seal foam." First result I found, there may be better ones more suited to what you want to do.
https://punishedprops.com/2016/09/20/sealing-foam-props-costumes/
I would find a place locally that does foam cut outs in large sizes like that, explain what you're trying to do and how best to achieve it. If you're lucky, they could do all of it in house. If not, they may be able to cut the foam, then recommend some other shop locally to either paint it or wrap it or whatever.