That's why you check it when the cable is on and you can shift it into the big ring. Try to decide, does it need to go up 1mm? down 2mm? Then try to reproduce that adjustment when the cable is slack, and check it again after it's wired up.

You can move the derailleur cage by hand with the cable detached, it's a fairly strong spring. You don't have to worry about breaking anything, just try to apply the force in about the same place the cable would be pulling, and then it's no different than the cable pulling it. Don't push way down at the end of the cage or anything.