The theory of general relativity says that "gravity" and "distorted space(-time)" are one and the same phenomenon. So it's a question of whether you believe that theory is correct.

We've known for a long time that GR predicts that when black holes and/or neutron stars collide, they should emit gravitational waves with a very specific shape. The LIGO and Virgo observatories detected faint signals that seem to match this shape, which gives us confidence that the theory is a correct explanation of the data.

This adds to the mountains of other evidence for GR, and complements it by showing that GR still holds in environments where space-time curvature is extremely strong.

Technically, we don't know for sure that it's impossible for GWs to be produced by other sources than moving masses, but we have neither theory nor evidence to suggest such a thing is possible.