This position has been used in hundreds of chess problems for various reasons by a plethora of problemists over many, many decades. It is known as "Vielväterstellung" in German, or "The Grandfather Position" as I know it in English.
However, how old is Grandfather? Find the fastest possible proof game to reach this position. The first answerer to provide proof of optimality receives the checkmark. Good luck!
I started with a different tactic than the first answer and made it to the same result, but between studying his and tweaking mine, I have now managed
41 plies
The game:
1.d4 c5
2.Qd3 Qb6
3.Qxh7 Qxb2
4.Qxg8 Rxh2
5.Qxg7 Rxg2
6.Bxg2 Qxa1
7.Bxb7 Kd8
8.Qxf7 Qxa2
9.Bxa8 Ba6
10.dxc5 Bxe2
11.Kxe2 Kc7
12.Qxe7 Qxc2+
13.Ke3 Qxf2+
14.Ke4 Qxg1
15.Qxf8 Qxh1+
16.Ke5 Qxc1
17.Qxb8+ Kxb8
18.Kd6 Kxa8
19.Kxd7 Qxb1
20.Kc8 Qb6
21.cxb6
General comments on strategy and whether it's optimal...
White's 21 moves include:
3 moves for the pawn (minimum), including 2 captures.
7 moves for the king (minimum), including 2 captures.
1 other non-capture move (Qd3).
I tried a few ways to have the only non-capture moves be from the king or pawn, but anything I tried resulted in black needing to make more than 20 moves. I was also hopeful to leave the black bishop on c8, but then the white king can't take d7. As the d7 pawn was pivotal in allowing the white queen to take the majority of pieces, I chose that.
I really think that this is optimal, but I don't have a good way to prove it. I do have to credit Albert's answer with giving me the idea to end with the black queen on b6, which saved me the one pawn move I needed to get past my problem of both black and white needing 21 moves, forcing my game to 43 plies.
UPDATE:
43 plies
1.d4 b6 2.Bh6 d6 3.Nh3 Bxh3 4.Bxg7 Bxg2 5.Bxf8 Bxf1 6.Bxe7 Bxe2 7.Bxd6 c5 8.Bxb8 Qxb8 9.Kxe2 Qxh2 10.Ke3 O-O-O 11.dxc5 Qxh1 12.Qxd8+ Kb7 13.Qxg8 Qxb1 14.Qxh8 Qxa1 15.Qxh7 Qxb2 16.Ke4 Qxa2 17.Qxf7+ Qxf7 18.cxb6 Qxf2 19.Kd5 Qxc2 20.Kd6 Ka8 21.Kd7 Qc8+ 22.Kxc8 *
This might be optimal but it is difficult to be sure.
White uses 22 plies to
(1) capture 14 black pieces
(2) move their king 7 ranks down the board
(3) get a pawn to 6th rank (min 3 moves)
Obviously, (1) and (2/3) are not mutually exclusive
Black uses 21 plies to
(1) capture 14 white pieces
(2) move their king 4 files (min 3 moves taking advantage of castling)
Calculating an exact minimum is difficult because
(1) some moves (for example blacks very first) cannot be used towards any of the listed tasks (2) any capture on ranks 3-6 can only happen after a piece moved there without contributing to any of the listed tasks
end of UPDATE
I'll get the ball rolling:
45 plies
1.e4 Na6 2.Bxa6 b6 3.Bxc8 c5 4.Bxd7+ Qxd7 5.d4 O-O-O 6.dxc5 f5 7.exf5 Qxf5 8.cxb6 Kb8 9.Ke2 Qxc2+ 10.Ke3 Qxb1 11.Kf4 Qxa2 12.Ke5 Qxb2+ 13.Ke6 Nh6 14.Bxh6 Qxf2 15.Bxg7 Qxg2 16.Bxf8 Qxh2 17.Bxe7 Qxg1 18.Rxh7 Qxd1 19.Rxh8 Qxa1 20.Bxd8 Qxh8 21.Kd7 Qxd8+ 22.Kxd8 Ka8 23.Kc8 *
No proof of optimality because I doubt this is optimal.
Here is one that ties @Joel's. I'm mostly posting it because it feels to me as if it has got some slack in it, so perhaps some one else can squeeze another move out of it:
1.d4 c5 2.dxc5 Qc7 3.Qxd7+ Kxd7 4.Kd2 Qxh2 5.Kd3 Qxg1 6.Rxh7 Qxg2 7.Rxg7 Qxf2 8.Rxf7 Qxf1 9.Rxe7+ Kc6 10.Rxb7 Bd7 11.Rxb8 Qxe2+ 12.Kd4 Qxc2 13.Rxf8 Kb7 14.Rxg8 Qxc1 15.Rxh8 Qxb1 16.Rxa8 Kxa8 17.Kd5 Qxa1 18.Kd6 Qxa2 19.Kxd7 Qxb2 20.Kc8 Qb6 21.cxb6 *
Similar, same number of plies but feels even more suboptimal:
1.d4 c5 2.dxc5 Qc7 3.Qxd7+ Kxd7 4.Kd2 Qxh2 5.Kd3 Qxg1 6.Rxh7 Qxf2 7.Rxh8 Qxe2+ 8.Kd4 Qxc2 9.Rxg8 Qxc1 10.Rxg7 Qxb1 11.Rxf7 Qxa2 12.Rxf8 Qxa1 13.Rxc8 Kxc8 14.Kd5 Qxb2 15.Ke6 Qxg2 16.Bxg2 b6 17.Bxa8 Nd7 18.Kxe7 Kc7 19.cxb6+ Kb8 20.Kxd7 Kxa8 21.Kc8 *
And another variation with
21 white plies and 19 black plies
1.d4 c5 2.dxc5 Qc7 3.Qxd7+ Kxd7 4.Kd2 Qxh2 5.Kc3 Qxg1 6.Rxh7 Qxf2 7.Rxh8 Qxe2 8.Rxg8 Qxc2+ 9.Kd4 Qxc1 10.Rxg7 Qxb1 11.Rxf7 Qxa2 12.Rxf8 Qxa1 13.Rxc8 e6 14.Rxb8 Kc7 15.Ke5 Qxb2+ 16.Kxe6 Kxb8 17.Kd7 Qxg2 18.Bxg2 b6 19.Bxa8 Kxa8 20.cxb6 NULL 21.Kc8 *
