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It is impossibe.

White would have to make an odd number of knight moves and black would have to make and even number of knight moves (or vise versa) in the same number of moves, and that it clearly impossible as knights alternate between white squares and black squares.
Of course it is possible. 1.Nf3 f6 2. Ng1 f5.
@StevenEmily

You know that 1.Nf3 f5 2.Ng1 works too, right? So many possible ways to get to that position.

After all, you never said black JUST moved the pawn to f5; white's turn could've just ended.
According to the fen it is white's move.
However, White could have played 1.Nc3 f6 2.Nb1 f5 as well.

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