This is normally done with a coring drill/diamond hole saw?
I suppose if you could get past the glazing with a tile spade drill in the center, you might be able to use a carbide coarse rotary file to spiral out from the center. Risky? Rent a coring drill?
If routing is your only option, get some other color tiles for practice. Maybe even route out a nest to hold the tiles in the orientation they will be on the wall when cutting the holes to get them located on center.