No pilot on this planet would ever consider a 1-engine take-off on a 2-engine aircraft.
Not so I'm afraid. Granted, not a 777 but a twin jet nonetheless:
https://aviation-safety.net/database...?id=19980319-1
PROBABLE CAUSE: "The pilot-in-command's decision to attempt takeoff with the right engine inoperative, resulting in his failure to maintain directional control or attain adequate airspeed during the takeoff attempt. Factors included a fractured right engine starter-generator drive shaft, resulting in an inability to perform a normal engine start on the ground."