Are there any legal chess positions that cannot be arrived at by a legal move from a legal position?
Thus there are no such positions. Every legal position can be arrived at by playing a legal move from another legal position. That includes the starting position, since Nf3 Nf6 Ng1 Ng8 cycles back to it.
I can think of several, for example if you had all 32 pieces on the board, but pawns were behind each other on the same file.