Yes, certainly the scientific method! And that same methodology has GR overwhelmingly accepted and matching observational evidence every day. The thing you need to understand about the instantaneous concept is that it goes against all we understand.
Even in Newton's day, and many years before Newton, the speed of light was known to be finite. Ole Roemer was the first person to measure that light travels at a finite speed. He observed that Jupiter’s moons and the moment they were eclipsed, took place sooner than when Earth was nearer to Jupiter then when Earth was further away.
Add that to the fact that light follows geodesics in spacetime, and the fact that gravity essentially is not really a force, just spacetime curvature and we have the evidence that gravity propagates at the same speed. The probably latest evidence of that would be gravitational waves.
https://en.wikipedia.org/wiki/Speed_of_gravity
https://www.discovermagazine.com/the-sciences/why-does-gravity-travel-at-the-speed-of-light
https://www.forbes.com/sites/starts...y-must-equal-the-speed-of-light/#77e2897a2fc0
"The
speed of those ripples is determined the same way the
speed of anything is determined in relativity: by their energy and their mass. Since
gravitational waves are massless yet have a finite energy, they must
move at the speed of light!"
The propagation of gravity is observed and must be at the speed of light.
It's great to be open minded and prepared to look at all facts and figures and alternatives, but its also great to know some basic physics and cosmology first.
If the cons go against established theories and observation, throw them out...it's as simple as that.
Again research some reputable links or ask questions in the sciences, rather then here where all sorts of ignorant agenda laden replies will be forthcoming...particularly from our friend river, who rejects totally and out of hand, all 20/21st century cosmology...even direct proof and evidence. That's why he is confined to the "nonsense sections'