It does begin to drop as soon as it leaves the muzzle, when compared to the mathematical line that includes the axis of the barrel and which extends out from the muzzle to infinity.
If the muzzle is aimed at a point five degrees above the horizon, the bullet starts to fall below that line the instant it leaves the muzzle. The bullet is still climbing with respect to a horizontal, but it is falling with respect to the muzzle axis.
When he said he aimed at a point 75 yards above the target, that does not mean that the round ever got 75 yards above the target, not even close.
Is there an echo in this room?