Are we talking something out of or into nothing? If the universe is expanding, into what is it expanding?
I thought space was infinite.
Maybe the universe is part of a greater expansion of multiverses, and as this one dissipates, 2 or 3 or 5 new ones will pop up to replace it.
We can measure whether light from distant stars is redshifted or blueshifted, because different atoms emit definite spectral lines in a clear pattern. If you line up the pattern seen in a lab from e.g. glowing hydrogen, with the pattern seen from a distant star, they are the same distance apart and the same line widths, but all moved toward red by the same amount. Ergo, that star is moving away from us, at a velocity we can measure by how much the light-pattern moved.
For nearby objects, some are redshifted and some are blueshifted, because they all have "proper motions" toward or away from us. But go far enough away, and there aren't any objects headed toward us anymore. Everything is receding, and faster and faster the farther it is away.
One might imagine this is because we are smack at the center of everything, and everything is specifically moving away from this one and only spot, at higher and higher speeds, because gosh nothing wants to be here.
But scientists don't accept explanations that "ad hoc". The other possible conclusion is that anywhere you are, you'd see that - because space itself is expanding. That is the current accepted theory, to explain the red shift seen in the color spectra of distant objects.
I hope this helps.