I’d use a diamond core bit .. in which case a smaller hole (bogger than the guide bit) won’t make any difference… (I’ve done lots using lab equipment) but at home for the taps/pipes I used a small 5mm core tile drill to make a pilot then whatever diameter the pipes needed
However depending how thick/massive this is I’d not think you’ll get anything clean with plugs and feathers as you are breaking crystals not a rock with a grain… I’d be making a starting point of weakness using a diamond bladed cutter (in fact did this today by coincidence with a 2″ thick diorite paving “brick”… then just a cold chisel and lump hammer and it split quite cleanly but that’s far finer grained than a granite.
LOTS and LOTS of Lubricant/coolant