Ah. I thought I solved it, but I forgot to count my moves on my fingers.

I saw up to king captures knight on c4, then thought that pushing the pawn to promotion of rook or queen (forcing black to move the h-pawn, as the king is without moves), then queen/ rook to a8#.

I didn't realize that took 7 moves to accomplish and got myself excited thinking that I solved it :(

Odds are that's how I would play it over the board if I didn't realize that this was a mate puzzle, especially in short time controls. I guess that's a sign that I need to start paying more attention to mating nets, as other forcible alternative mates obviously aren't always present in these types of positions (= losing winning positions).