Are there any legal go arrangements that can never occur in an actual game?
Assuming you're only interested in what's on the board and passes are allowed.

I would go backwards then: what was the position just before?

It's quite easy to see that if you remove any stone of any colour from a legal position, it will still be legal.

So in deciding what was the last move, pick any stone of the player whose turn just ended and assume that that stone was placed without any capturing.

If the number of black and white stones is too different, include a sufficient number of passes for one player.

In other words, the way to get to a given position, the players just have to place their stones (in any order) to where we want them to be and nowhere else (with a certain number of passes if necessary). No capturing will happen then.