The original bellows/butterfly thermostat (no longer made) had a bleed hole in the middle of the flap.
The current stock replacement thermostat has this bleed hole to let air through when filling with the "jiggle pin" that closes when water pushes up against it so that no flow can pass.
That thermostat is on the left. A better modern replacement with a much higher flow is the Stant thermostat on the right.
If you look very closely at the edge of the moveable valve plate on the Stant stat you will see a small indentation that allows air to pass through when filling eliminating the need for a bleed hole. Look closely at the edge of your thermostat and see if it has the same indentation. If so, you don't need to drill a hole. If not, I'd drill the smallest hole possible - 1/16" - to let the air through when filling.