You sound like you know what you talking about, we should talk. Yes, the core could be cork or even non natural. I just don't want to interface with synthetics.
I don't know if one can foam natural rubber to the same fine consistency as crocs. I'd probably create a solid shell and then add the foam inner sole if I were to design it.
Also: no shortcuts, unfortunately
https://www.wevolver.com/article/3d-printed-rubber-whats-possible-and-what-isnt
> Is it possible to 3D print rubber? In a strict sense, no. But with a huge number of flexible filaments and flexible resins out there, it is possible to make pliable, rubber-like parts suitable for a range of applications.
Discussion
I'm open to that! I'm a mechanical engineer, and I have just enough materials science knowledge to be dangerous 🤙
The difficulty you'll find with natural rubber is that it can't be reworked after vulcanization, the hardening process, so you'll need a mold for the whole shoe. You could 3D print the positive, use it to make a negative with a temperature resistant material, and then cast and vulcanize the rubber in that negative. Rinse, repeat.