Is it at all possible that instead of being pushed away, we are instead getting pulled toward something huuuuuge via gravity? As if we are falling into something way greater than ourselves? I thought this was a wild idea but after I Googled it I found out that there is such a thing as a “Great Attractor”. Something 150 million light-years away is literally pulling all nearby galaxies towards it but no one knows exactly what it is.
So how do we know there aren’t any other Great Attractors, Greater Attractors, ad infinitum?
You are right that things would still look like we're accelerating away from us, even if we were actually contracting.
Interesting hypothesis! How do we investigate?
What could we expect from a large central gravitational point? We should have other signs of the gravity well:
We would expect a point that we contract towards (and that seems ill fitting, as we see the expansion moves as the observer (including earth) moves), we would expect some kind of mass or similar effect, which would also have a size to fit it in (we know that gravity works different when you're inside the mass, and we would be able to see it, much like black holes or dark matter), we would expect things to orbit the gravity well (which we know that at least our galaxy doesn't orbit us).
You might want to actually check on these things to make sure they apply and are true, but at least at first glance it seems the expansion is better explained without a central gravity.