Dumb question: why did we need to see far-away galaxys moving away faster than near galaxies to conclude that the universe was expanding? Wouldn’t just the fact that everything is moving away from us lead to the same conclusion?
Imagine inflating a balloon onto which you've painted dots. All the dots move apart. But the ones furthest apart move apart faster than those close together. This is how you know the dots aren't just moving in their local environment, the entire space is expanding (everywhere).
(If you want a 1D representation, move your fingers apart at a constant rate. Consider how much further apart your pinky and index finger are compared with your middle and ring finger. That wouldn't happen if you just make a Spock hand.)