In my opinion Rc6 looks like the best move, no engine required
That was my first reaction. (I don't use engines).
I've been staring at that board for a few minutes to figure out why that is the move and I THINK I figured it out, so correct me if I'm wrong.
You sacrifice the Rook at c6, it is taken by the pawn from b7 to c6. your pawn on d5 recaptures the pawn on c6 threatening the Knight, the Knight moves to I think b6 threatening your Queen, you take with your Bishop from e3 to b6 and the Queen takes your bishop on b6 you then push the pawn to c7 and... checkmate. Discovered check and the pawn covers the only escape square.
In my opinion Rc6 looks like the best move, no engine required
That was my first reaction. (I don't use engines).