We run a Calypso Hammerhead machine. When cutting either granite or quartz we sometimes get a blowout at the pierce point. How do we get it to either pirce gently so as not to get a blowout on tne material or to get the machine set up to pierce outside the pierce point and move in to the actual cut?

You have a couple of things you can try.  Preload the cutting head with a little abrasive and try it at low pressure.  or lay a piece of scrificial over the top just for the pierces.  The sacrificial will take the impact so it does not chip.  the second can get kind of expesive if you do it alot (this from experience). I am not familiar with the calypso machine to even know if this will work but another option you might try, contact someone at Flow to see if they have a retrofit option on their ultra pierce vaccum.  We use it on ours for cutting glass and find it to work pretty well.

If you're using geomate, you should ensure that "leaders" are turned on.

I'm shocked you haven't always used them, if you use "arcuate" leaders, you can get really quality parts where you've probably been getting terrible notches.

You can also try low pressure pierce, just select it on your cutting options and follow the onscreen instructions.