I’ve had one of our hens sneeze out an egg in front of me once. I had brought treats out for them and she ran out of the nesting box then started gobbling up. She paused from eating, stood up, and sneezed. Out came the egg, landing unharmed in some shavings. Ate it for lunch the next day. Never had it happen before or since.
When I rescued my Golden Comet, she jumped into a potted plant (completely ignoring the fancy nest box), stuck her bum out over the edge, looked at me, squawked, and laid an egg - right in front of me. The egg fell over the side of the plant and broke on the ground. This was MINUTES after I brought her home. Musta been holding it in during the car ride.
Oh, and that very same hen took a trip to a renowned avian vet in the region and he had a tech hold her head and neck against the tech’s chest and stretch her feet out toward the floor and the vet pushed on her abdomen and popped an egg right out of her. When I went to pay I sat all the meds and stuff on the counter and the secretary just blinked and was like why do you have an egg??