With a one-off precomputation you can do a lot. If you store the distance to exit in each cell you can introduce a slight bias towards the exit. Easy to implement but not very realistic since it assumes things the guests can not know.

More realistic would be observing that the entry and exit are on the outer edge and the maze is simply connected, so a trivial left-hand rule [1] will solve the maze in linear time. On its own pretty boring. You could ad some randomness to make it interesting. But would it still have linear expected solving time if you do that?

[1]: https://en.wikipedia.org/wiki/Maze_solving_algorithm#Wall_fo...