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Backtracking.

1. Place a mechanism which aims at the goal from a random direction and a random distance. Have it face randomly so the ball needs to come from either the right or the left to get directed to the goal.
2. Then another one at a random distance which aims at the previously placed mechanism's input, again with its own input randomly facing right or left.
3. Repeat step two. The number of iterations depends on the desired difficulty.
4. Place the start so it faces the last placed mechanism. You now have a solved puzzle.
5. (optional) place some more random mechanism which aim at the opposite of the output of a random one of the existing mechanisms. These are "red herrings" which are not needed to solve the puzzle and only serve the purpose to confuse the player.
6. Then rotate each rotator into a random direction so the player has to guess how to rotate them.