This puzzle has the problem that I don't know if black can castle or not. I thought not so that lead me thinking that Bg5 is sufficient to win (it is not because black escapes a critical sequence by castling).
I think if the "can castle" state is not known but needs to be known to analyze all variations, then it should not be a legitimate puzzle.
I think if the "can castle" state is not known but needs to be known to analyze all variations, then it should not be a legitimate puzzle.