In retrograde analysis problems, castling is assumed to be allowed unless it could be proven that either the king or the rook has previously moved.
It is well known, of course, that one could never be sure whether castling is allowed if the king and the rook cannot be shown to have previously moved, since one could simply start the game with silly moves of the knights and rooks for the sake of disabling castling.
Namely, one could just do the following silly moves of the knights and rooks for the sake of disabling castling on both sides (do only the first four moves to only disable kingside castling, or only the last four to only disable queenside castling):
- Nf3 (or Nh3) Nf6 (or Nh6)
- Rg1 Rg8
- Rh1 Rh8
- Ng1 Ng8
- Na3 (or Nc3) Na6 (or Nc6)
- Rb1 Rb8
- Ra1 Ra8
- Nb1 Nb8
Now, suppose that one requires the first move by each player to be a pawn move, implying that the initial configuration of the pieces could never be repeated regardless of castling rights.
Then, with that opening requirement, could castling ever be proven to be legally allowed for sure?
I think that the answer is still no even if the first move by each player is required to be a pawn move rather than a knight move.