Some of the most precise lasers built are repeatedly bouncing light over miles in a tunnel to track changes in arrival significantly less than a trillionth of a second different.
Doing this while filtering out noise from miscalibrated sensors or just small vibrations outside the chamber is HARD, but improving. It gets better as more come online around the world to confirm detections and aid in better directional targeting.
“...Concluding on a lighter topic, let me remind the GGP community of what I recall as probably the most memorable moment of the first campaign. It occurred at the GGP Workshop in Munsbach Castle, 1999, when Virtanen was describing the effect of snow cover on the residual gravity at Metsahovi. He showed a figure of gravity increasing by about 2 microgal over a 4-h period as men shoveled snow from the roof of the SG station, when a member of the audience asked why there was an interruption in the rise of gravity, Heikki said this was a 'tea break'...” D. Crossley, in Journal of Geodynamics 38/3-4 (2004), p. 234.
Every time you lift an object, you are overcoming the gravitational force of an entire planet. Gravity is that weak.
Meanwhile, the incredible destruction caused by a nuclear bomb is the product of the energy stored in just a handful of atoms.
The point about how we can only infer their existence from a mass of data is similar to how we talk about deep learning. The pretrained neural net works, but we can't pinpoint why, we can only test it on various data and receive results.
There is no "dog that didn't bark", because we clearly can see the graphs and the correlations.
The way we detect gravitational waves is not "the photon haven't arrived", but "the photon has arrived a few nanoseconds earlier than we expected it". (But multiplied by a few thousands of reflections and detected only by interference pattern, not the photon arrival itself).
So, in a way, it's similar to deviations from paths by which we presume dark matter. But also, it's not that: we are almost certain here that these exact deviations are caused by the gravitational waves, because calculations and because multiple unconnected detectors, and because the form of the graph matches.