There is no covering under the garage floor.
You don't have to drill the trough the frame rails, the floor is 1" thick and through bolting will more then suffice. You are only using the the chock to support the bike, the straps do all the work.
There are 5 frame rails that run under the garage floor, so the odds are good that you can at least catch one side of your chock with a rail.
I "use" to keep my BikePro chocks bolted down to the floor. I bought a Condor last year and had that bolted down for half the season. I now just keep something in front of the Condor to keep it from sliding forward, usually my refrigerated cooler.
My bike is 800 pounds and it never moves.
I do have multiple attaching points on the floor, I use aluminun load track, have three pieces going front to back and one each across the front and rear of the garage.
Horrible freight is not the place to buy your tie down straps if you value your bike.