“For example, if I know the current position and velocity of an object falling under the force of gravity, I can calculate where it will be at any time.”
But you can’t predict with certainty where it was even 1 second before it began to fall.
Well, you can if you know the position and velocity of every object in a closed system, or even an open system if you know that for all objects in the universe, by working backwards in time in this case. That's the point of classical, deterministic physics.