[slavik81]

Get a block of styrofoam, slice it in two, and carve out a hole between the blocks exactly the size and shape of your egg. Tape the blocks together with the egg in the centre.

It is incredibly effective to have a solid surface in contact with the whole shell. And, the outer styrofoam will absorb the worst of the landing. It's also very light, so it minimizes the energy that must be dissipated.

Lesson learned from my failed attempt at the egg drop in high school. The guy with the styrofoam absolutely destroyed everyone at that challenge.

[dmonitor]

Even simpler: A barrel of water densified such that the egg floats in the middle

[slavik81]

That was the solution employed in the ActionLabs video linked in another comment, but you'll note that their first attempt failed with that approach.

It's difficult to prevent any container that heavy from breaking open when hitting concrete at terminal velocity. I'd bet that the styrofoam block could be dropped from any height and survive landing on any surface, no matter how unyielding.

[sdeframond]

How about soaking the egg into epoxy resin ?

[BobbyTables2]

That cracks me up!

Even if the egg doesn’t survive, nobody will ever know!