I wonder if there are bucky balls full of helium hanging out under pressure in there?

I found this similar idea done in a lab: https://cen.acs.org/articles/83/i3/Filling-Fullerene.html

They use H2 instead of He. Is that good enough?

Indeed, unimaginable what is possible! There will also be traces of H, N, O, S etc due to comets crashing in, so room for carbon chemistry once temperature permits.