I might add that I commonly find "adjusted" shifting systems where the shifter hits low gear with the chain still in the middle of the cog stack.

Some serious cable-tensioning MIGHT fix it.

Also, note that the exact routing/placement of the inner wire (cable) at the anchor bolt (pinch bolt) can affect the ACTUATION RATIO of the derailer, and thus must be exactly as intended (in the groove) for the indexing to move accurately in response to the shift lever's movement.

Also check for smooth movement of the cable. Tug on the exposed length of cable running alongside the frame tube. The cable should move and recover it's tension as you let go of it. The action should be smooth and friction-free.