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?
Others have mentioned, everything is moving away from each other, like the surface of an expanding balloon. But that is what we observe, and there is more beyond the observable universe.
There is an idea that our universe might actually be in a black hole in a higher universe. To expand on the balloon simile (pun intended), this would be like a balloon expanding uniformly except in a spot, a bubble appears and expands faster. A bubble within a bubble. Kind of a tumor, an outgrowth universe. Hope I've been illustrative enough.
It's not exactly what you asked, but a higher level black hole is kind of something pulling all matter in our universe instead of pushing.