It is possible to reach (exactly) #8 after just 3 moves:
[Title "#8 after 3 moves"]
[FEN ""]
1. e3 f6 2. Qf3 Kf7 3. Nh3 Qe8! 4. Ng5+ Kg6 5. Bd3+ Kxg5 6. Qf4+ Kh5 7. g4+ Kh4 8. Qg3+ Kg5 9. f4+ Kh6 10. g5+ fxg5 11. Qxg5#
Is there any longer forced win than #8 that can be reached (and proven) after just 3 moves?
This question is a variant of, and therefore not a duplicate, "The quickest mate in n."