Consider a chess variant which plays exactly (*) as chess except that the players have a special option for first move.
White can, instead of moving a pawn/knight as its first move, sacrifice any of its pawns (removing it from the board) to reorder its pieces (within the first rank).
Then, Black has almost the same option: it can reorder the pieces instead of moving a pawn/knight, but a sacrifice of a pawn is optional.
Would it be advantageous for White/Black to pursue this option instead of a regular opening move?
Which would be the best options for sacrificed pawn and permutations of pieces?
(*) For castling: if the king is between the rooks, castling follows the rules of Chess960/Fischer Random Chess. If it isn't, castling is forbidden.