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That's not quite right. Even if there were no gravity or other forces, there would be no incentive for matter to go in one direction vs another, regardless of the distribution of matter around it. Over time you'd get a uniform-ish distribution, but that's a question of statistical mechanics, not one of pressure differences.

On earth, matter only rushes to fill vacuums because the surrounding air or water pressure pushes it in.

Vacuum doesn’t necessarily mean pressure-vacuum. It roughly means extreme concentration gradient, which is as you’ve described universal.

> but that's a question of statistical mechanics, not one of pressure differences.

My limited understanding was that 'pressure' is just a simplified way of speaking about statistical mechanics.

If all of the matter in the universe were evenly distributed, it would be so close to a vaccum as to make no difference.

Don't forget, even within individual atoms, the overwhelming majority of the space is a vacuum.