How Long Before an Egg Starts to Stink?
Years ago there was a related question, How long can eggs be unrefrigerated before becoming unsafe to eat? .  In that one, we're looking at how long are they safe (which means a very low probability of them being spoiled).  But one of the answers links to an experiment from the 1970s by Mother Earth News.  

In the article, they mention that they abandoned the unrefridgerated eggs (both store-bought and fresh laid) were still edible (but not great) at 90 days.  But another month in:


  By June (120 days after the experiment was begun) all the supermarket and all the homestead control eggs had gone completely rotten. 


But not to worry, you don't have to wait 4 months:


  Our experiment was set up on February 4, 1977 and was designed to run for a full year of regular monthly "look, sniff, taste, and texture" tests. It very quickly became apparent, however, that some of the "preservation" methods we were trying were worse than no attempts at preservation at all. The eggs (both fertile and unfertile) buried in both the wet sand and sawdust looked bad, smelled bad, had lost their taste, and had runny textures just one month after being "preserved". Even the control groups — eggs which were just allowed to lay out at room temperature with nothing done to them — were better than that. Conclusion after only four weeks: Trying to store eggs in either wet sand or dry sawdust is counterproductive. Forget it. Anything else — even nothing at all works better.


30 days might not be enough to get that really horrible smell.  I'd probably go for 45 to 60 days in wet sand or sawdust.  I have no idea if playground sand would be better than sharp sand for this, but I suspect that if you're doing this at a colder time of the year, you might want to give it a couple of weeks past that, just to be safe.

You can also pack up a dozen eggs, and then after 30 days (not weeks), check one.  Then again every week or two until you get what you're looking for.