There is clearly some finger trouble here. On the 777 the policy is to rotate towards 15 degrees and once airborne follow the flight director. After the Air France incident the software logic was changed so that the autopilot could not be accidentally engaged on the ground when moving. However the autopilot will engage in the air below 200 feet and if 0000 is in the MCP window then it will fly level and descend. However there should be a very distinct "Don't Sink" aural that repeats.
Additionally if the flaps are approaching flap limiting speed the thrust will reduce automatically from the derated takeoff thrust setting which will not help the situation when close to the ground.
The autopilot is normally engaged by the pilot flying, not the P2.
I await further details with interest.