Last time I checked, the motion and recording were tied together so you can’t record without motion being detected and you can’t detect motion without recording.
With the free unofficial DH and SmartApp, you could arm the camera when someone steps on the mat, but it would still need motion to start recording. By the time it armed, detected motion and recorded, the person probably would have already left.
The Blink API isn’t public yet so the free version doesn’t have Live View, but I think the paid Official Blink version has it. I’m not sure if it provides a way to automatically turn it on, but @RBoy should be able to answer that for you.