Well the black h-pawn must have promoted as to move the white pawns into position needs seven captures on e3, f3, g3, f4, e5, d6 and c7. Black is eight men down, as the c8 bishop can't have moved that leaves those seven captures, the one on c7 must be the original c7 pawn.
The pawn on b4 is therefore the a-pawn, and the pawns on d6 and e6 must have arrived via captures from e7 and f7 respectively. Which are the white N, B and Q.
Pc7 = Ph2. White made 7 P captures and Bc8 was captured at home.
Pd6 = Pe7. Black made 3 P captures.
Black's only got a few moves left to retract, so the start is forced.
-1.Bg2-h1 a5xBb4 -2.Bf1-g2 a6-a5 -3.g2xRf3!
A screen on the 8th rank is needed, but it is not yet clear why it must be a Rook.
-3...Rf7-f3 -4.R~-h7 Re7-f7 -5.R~ Re8-e7 -6.Kh7-h8 Ng6-f8+
The rest of the sequence is easy enough to see without going move by move. wR, K, B return to a1, e1, c1; f7xQe6 puts wQ back, she returns to d1, d2xBe3 puts bB back, he returns to f8; e7xNd6 clears the way for wPc7, and the next uncapture must be d6xPc7, because bPc could not have left the file.
So why was the 2nd uncapture a Black Rook? Answer: An R cannot get back to a8 unless he does so before all the Black pawns retract.