Dolly's Puzzle No1

Yes, Kg3 Bc7+ Kh3 then there's nothing that can be done and move the knight Ne2 Nf4 for checkmate

After Kg3 even if Black plays Bxg5 hxg5 Kxg5 we have an endgame in which White is clearly winning. With one way or another, after Kg3 White is winning.