The resolution of the detector is 1/1000th the width of a proton. The signal they see is much bigger: the length of 4km long arms stretch and then shrink about 1/10 the width of a proton. How do they know it is really space/time changing and not an earthquake? They have two detectors over 1000 miles apart from each other:
https://en.wikipedia.org/wiki/LIGO#/media/File:Simplified_di...