that implies that garbage within the container is evenly distributed.
Yes grass tends to be more evenly distributed than most things. If you think about it you are restricted to a sensor that detects a level or one that detects mass. A mass detector is rather tricky to retro fit to such a large container.
What do you mean with "equivalent of an arduino board with discrete components." ?
I mean making what circuit is on an arduino board but with your own parts. That is the only way you can integrate a sensor onto a board. Otherwise you will have to just attach the sensors to the board. Which might be what you meant but not what you said.