An Interactive Proof of God's Number?
... it seems the Decision problem "God's Number is &lt; 20" lies in $\Pi_2^p$.


That is enough for it to have an interactive proof. In fact, Lund et al. proved that every language in polynomial hierarchy (PH) has an interactive proof by using Toda's theorem ($\rm{PH} \subseteq P^{\#P}$). They reduced $L\in \rm{PH}$ to #P-complete language PERMANENT, and provided an algebraic method which can be used to prove PERMANENT interactively. (This is highly inaccurate; please refer to the paper for more info.)

Using their techniques, Shamir proved that IP=PSPACE.

It was previously proved that all IP has zero-knowledge proofs, so:

All languages in PSPACE have zero-knowledge interactive proofs.