Tap the center pins of the rivets so they are flush with the rivet body.
Use #10 x 1/2" Stainless Steel Screws to affix the plate to the mounting bracket. You can see slight indentations where the screws are to go. I drilled pilot holes first.
Don't use the "standard" license plate hardware that is 3/4" long. Those screws appear to be long enough to hit the bumper when inserted.