1. There's no tricky business with en passant or castling here. Everything moves like it should.
2. If we disregard the legality of the position and try to find a cooperative mate, then white's next move must be Ke6. g5 is the only other possiblity, but this inevitably leads to a draw.
3. Thanks to the the white g4 pawn, the pieces can be manipulated so that the resulting position is almost the same, but with black to move and with the white pawn on g5.
I haven't been able to find a mate. Since I had no ideas here, I just tried to analyze it by brute force. All lines I tried ended in a draw.
However, I think the position must be "alive" for two reasons. First, the puzzle says it's "white to move". If the position were dead, the game would have already ended, and white wouldn't be "to move". Second, these puzzles are supposed to surprise, and this position being dead is no surprise.