LTC6993-1 Circuit not working
The circuit works as expected. The problem is probably your understanding of what a "Monostable Pulse Generator (One Shot)" is. 

If TRIG is set to a fixed level you will never see any output.

The output goes high only if a rising edge is detected at TRIG and then it stays for a given time. That's what a monostable (one shot) does.

EDIT:
Maybe the confusion came from the fact that this IC contains an oscillator to implement the one-shot functionality by a digital counter.