Time "exists" in physics in the same way everything else in physics does - namely, the value we measure with clocks in the real world satisfies all of the same

Time "exists" in physics in the same way everything else in physics does - namely, the value we measure with clocks in the real world satisfies all of the same properties (at least in certain regimes of the universe) as the thing we call "time" in various physics theories like relativity/classical mechanics. And those theories make (reasonably) correct predictions about the values we measure in the real world. Is it possible that these properties are the result of some other interactions that have very different laws at a lower level? Absolutely! But the discovery of particles didn't cause the sun to disappear, if that makes sense.