Solution

Congrats to @juanmi96 as winner of this round! :)

The fastest win for white was to play
1. Nf6+!

a)

After 1. ... gxf6 white wins rather fast:
2. gxf6 and black is completely helpless.

b)

After 1. ... Bxf6 the game continued:
2. gxf6 Bxg2
3. Qg3! g6
4. Qh4! Bh1
5. Rf2 and black resigned as he had no reasonable defense against Qh6 followed by Qg7#

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End position:

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By the way, the longest (not the most beautiful) variation is:

1. Nf6+ Bxf6
2. gxf6 Qc7
3. Qf4 Be4
4. Bxe4 Qxe5
5. Qxe5 Rd5
6. Qg3 g6
7. Bxg6 Kh8
8. Bh7 Rg5
9. Qxg5 Kxh7
10. Qg7# (checkmate)