...e4 - e3
I think that’s a good idea, the e3-e2 etc. Go for the promotion. White can’t stop it for several moves without losing Rook, Queen, or even both. If White moves the Rook up to c2 or c3 to try, Black goes Qe1++. If White brings the Rook over to e1 to threaten that pawn, Black plays Qxe1++. If White moves the Queen to c3 to get ready to kill the pawn when it promotes, then Black plays Qf1+. White has no choice other than Rxf1 to counter, and then Black plays Pxf1 -->Q -->++ (I don’t know what symbols for promotion are).
Nice solve Samoore. We overlook the lowly pawns too often.
When a weak back rank is mentioned, start looking for the checkmate… just a suggestion.
...b7 - b5
Get the White Queen off the diagonal, and mate follows.