Need to fill in details.
is the block mounted already?
Do you have a holesaw?
Variable speed drill?
It can be done with a few supplies.
Make sure that your block is firmly affixed to something.
Get some Silicone Carbide 80 grit rock polishing compound from a hobby store.
Drill a pilot hole first with a diamond bit , 1/4 inch should be fine.
Build a dam wider than the 3" needed for the hole, from modelers clay, Around the pilot hole (centered).
Also need a 3" holesaw, now place a little SC grit and water paste, in the dam area, And use the variable speed drill to slowly bore the hole, caution, keep adding a little more SC paste and water to cool things off.
This will get messy with the water, paste, and cuttings, needed to be removed from the groove, but with care and diligence, you will get it done.
Slow and light pressure on the holesaw, and you won't break it to crumbs.
Of course your holesaw will be ruined, so buy a low cost one.