The hole in the center is about 1/2 inch.

 

I think you would notice the lose of something like this or even see the difference in height of the radiator if it were from that? but regardless of that its a mount of sorts so noise would be heard so I doubt its from your car

 

That looks like maybe it is part of the belly pan- that plastic cover under the car. I noticed the top (facing the engine) has pieces that look like that on it (possibly sound deadening?). A piece might have broken off and just fell out.
Next time you change the oil, look at the plastic belly pan and see if it fits.

oops, just read that you don't have a stock belly pan? dunno then...

 

A few months ago, I replaced the clutch and flywheel on my car as well as the t-belt. I don't recall coming across a piece like this one at any time.

I checked my radiator, and it is sitting firm.

The only things making noise on my car lately are the front suspension and the exhaust (only on hard right-hand turns).

 

no

 

The only other cars it could be off of which were parked in the area are an 06 exploder and a 70s MGB

 

The only thing i could think of is a mudflap. But i dont think thats off an audi.

 

Update:

99% chance it came off the truck which plowed the driveway a few hours earlier.