Things I'm noticing in position:
- b3 is an important square. If unguarded white has Bb3+, Ng6+, Rh4#
- White also has a potential Qxa8 but king is currently in the way.
- Black wants to Qxh1 but can't at the moment because of point 1.
Kg3 has to be the first move clearing the diagonal while also keeping 4th rank clear for the rook.
Black's possible replies:
- If Rd8 then Qd5+, Rxd5, a8=Q
- if Qg1+ then Kh3, Qg4+, Kxg4, Qxh1, Bb3+, Kh8, Nf7+, Kg8, Nd8+
- if h6 then Qxa8+, Kh7, Bb3
- Qxb3, g6#
- Bxe5, Qg8+, Kg6, Bf7+
- if h5 similar to h6 but black can try Qg1+, Kh3, Qg4+, Nxg4, hxg+, Kxg4, Qg1+, Kh3, with white Qg8+ to follow.
Rather good ... but not complete - check the solution above!