Several options, all the suggestions above are good. If you use the “sandwich and drill” method, use a similar sacrificial material (I.e. not aluminum) or the bit will wander. If you choose to bore it (lathe or mill), then the material for the other half of the sandwich does not matter.
Pretty straight forward on the CNC. If it were me, locate the hole center (say X0, Y0), then a G176 or G177 - depending on the end mill size and if you drill a through hole first (only if your controller supports those codes).
Obviously the trick is to hold the part. Do not use the left or right end of the vise jaws - nearly all mill vises, the moving jaw will have a little bit of tilt (I can’t speak for all brands - just Kurt DX6, Kurt Anglock and PrattB HiLo - all are good kit). You can put an equal size piece in the other side (like when you are cutting a short piece in a cut off saw), better to use the mid point of the vise jaw. Then you will need a sacrificial pad, or hold the part about 60% sticking up - do half, flip it, do the second half. Or, here is your excuse to get some Talon grip jaws - set the teeth wide and come down to within a whisker of the jaw.
Let us know how you work it out.