I’ll go with @Customer and assume that you are using the WCO. Like they said, the delay (if it’s the wco) is due to the camera having to wake up and start recording. Pir sensors work better with side to side motion, and it looks like once the subject is within the pir range (25-30ish feet) they are walking towards the camera. That may also be a contributing factor to the late start. Unfortunately I don’t think anything can be done about the license plate, but you do have a good shot of the perps clothing/physical description and the vehicle make and model and color.
Here is a link to Lifehacksters wco video, and at the 8:00 minute mark starts displaying a license plate at different distances from the wco he is demoing. Even with the plate being faced straight at the camera, at 35-40 feet it’s indistinguishable.
Now it looks.like the distance from your cam to the perps vehicle is about 50 or so feet and at an angle, which is not gonna be able to get you anything at 1080p.
My thought to.improve your setup is try and get a camera that is powered by your home electricity (continuous record capability, faster detection), more telephoto than wide angle for a better shot of the end of the driveway from the house. Just some food for thought. Sorry you got some packages swiped.