SpaceCadetSpu
Black knight g3 check, white pawn forced to take knight at g3, black queen takes pawn at g3, and if I'm right then white's best move is to move queen to e5 which would trade white queen for black knight. the alternative moves for white in that situation result in mate for black or losing the queen without trading for a knight. You are right though, the better move is to move queen g3
I underlined in your post where I see something else
Once Black Knight to G3, White Pawn F2 Has to capture on G3
If you move Black Queen to G3 and Capture White Pawn, you get
White Pawn on G2 capture Black Knight on F3
At this point the Black Queen is alone and cannot force a checkmate. However, he can capture the 2 pawns on F3 and H3 as compensation for losing both of his Black Knights. White is not in the best situation because his King is very exposed but I would trade 3 pawns for 2 knights and take my chances as White.
The black queen isnt alone, there is a rook on b6 ready to jump. After White captures the other knight on F3 Rook to G6 is mate in 4.