Can you think of a scenario when the kinetic and gravitational potential energy could both be zero

-- Kinetic energy is proportional to the object's mass, and to the square of its speed.

If we want zero kinetic energy, either the object has no mass, or else it's not moving.

-- Gravitational potential energy is proportional to the object's mass, to the acceleration of gravity, and to the object's height above the reference level.

If we want zero gravitational potential energy, either the object has no mass, or there's no gravity, or the object is AT the reference level.

Here are some possible ways to make both kinds of energy zero:

-- The object has no mass. Very unlikely, because then, you have no object.

-- The object is not moving AND there's no gravity.  Very unlikely, because there's gravity everywhere.

-- The object is not moving AND it's AT the reference level.  This is the only one that makes sense.  It could easily be a stone lying on the ground.