It is a winning position, black will lose for sure.
The only critical move is 1. ... gxh5, because after every other move black simply has lost the knight, while his position is still bad. Therefore it is logical and most interesting to examine first what happens after 1. ... gxh5 which ends in a forced checkmate. Nobody wrote that white will always win within 13 moves.
You wrote the "Fastest solution". I can find a faster solution if I played both sides.
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As all the discussion was about 1. ... gxh5 (and that rightly so), @iceblue found the fastest solution against that move. Of course white wins also against every other black move.
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