How to prevent vermin from entering garage via space under garage door?
Install weatherstripping on bottom of garage door. From the pics, I can't tell if the garage door rolls up or swings to open. 

If the door rolls up, the weatherstripping can be installed on the very bottom of the door. Weatherstripping comes in various shapes and thicknesses. Filling a 1 1/2" to 2" gap seems excessive, but possible. 

If the door swings, then the weatherstripping will rub on the floor so you need a threshold mounted on the floor and directly under the garage door. Then you can install weatherstripping on the door and have it "reach down and touch" the threshold. So, when you swing open the door, the weatherstripping will "come off" the threshold and not touch the slab. 

Remember, those vermin can squeeze through a very tiny hole, COMPLETELY fill the gap.