My 64 had rubber plugs in the mounting holes from the factory as belts were optional.
You should see them from under the car 2 near the transmission tunnel and directly across not far from the rear of the front seat mounting bolts. The rear are located near the rear frame rail floor to the inside of rail and where the trans tunnel ends.
So no holes in the rug from the factory. 60 years later things may have changed form previous owners.