Assuming it is White that mates, Black must have made 5 moves.
Play might go
1. e4 a6
2. Bxa6 Other move
3. B move Ra4
4. Some move Rc4
But I can't see what Black can do with just 2 moves.
Otherwise he requires 4 moves to move his rook to c4, 1 move to move his king onto the a2-g8 diagonal, and at least 1 pawn move in which case it is impossible.
Therefore the Black king must be mated by discovered check (possibly using the White queen), but this seems equally problematic.