If light speed was infinite. If sound speed was infinite. Or even if water waves were infinite, we'd never feel or see anything waving.

We feel a wave by seeing the differential effect of it propagating. Which requires speed with a detectable progression. Compression, decompression. Excitation, de-excitation.

So when everything is quaking, we detect it by neighboring regions not being in sync as to the direction, amplitude, phase etc. of where they're quaking at any given moment.

Just like with normal earthquakes. The ground is shaking. If everything atop shook in perfect sync, you'd miss the earthquake. But otherwise, you feel it, you're destabilized. Not in sync with the ground.

For gravitational waves, it's much harder for us to feel it without special, very sensitive equipment. Normally. But if it was strong enough, we would.