Based on the photo, it looks like they are using some unconventional materials.

https://dabble.co/denver/painting/classes/craft-create-night-stamps-with-denver-public-library

At first I thought they were carving on cork--that's awful, I've tried it. But it looks like they have the stamps glued onto the end of a cork. Hmm, maybe that's what I can use my corks for. I'm definitely not carving on any more.

That was my first impression as well, but it looks like a thin layer of material (can't tell what it is, to be honest) that's glued onto a cork. And of course, it's possible that this is just a stock photo.

Maybe it's foam, but they look rather deep for foam. Actually, I think it is foam.

Possible, but on one of the stamps, the stamp is bigger than the edges of the cork it's mounted on, so I wonder if the edges of the stamp would make a good impression. Maybe it stamps poorly and they don't care about that.

That's probably it.