Wouldn't it make sense that we don't see any signs of life through the way how we currently observe the universe, but could see NHI tech on Earth, because of Relativity?

So, seeing a bunch of astrophysicists saying that they don't believe NHI has visited, we don't see any signs of life out in the universe currently, the question of the Fermi Paradox, etc. But with Einsteins theory of relativity and how we, as humans observe the universe through photons and wave lengths, doesn't it make sense that we aren't seeing any signs of life because what we're seeing in the sky/through our current tech is the past? The information we are digesting from these planets and...