On the other hand, the ancients assumed there had to be big continents in the southern and western hemispheres to "balance" the land in their own quadrant.

They turned out to be right, but not quite for the reasons they put forth.

As a non-cosmologist, I'm unwilling to speculate on what "should" be out there, because my mental model is probably very wrong (keeping in mind that our best models of what's happening out there are also probably quite wrong).

Well, in more formal terms, cosmology has the 'cosmological principle'[0], which is a conjecture that at large enough scales, the universe is universally isotropic and homogenous wrt the distribution of matter. Basically that it should average out to the same density everywhere, and should look basically the same in terms of how much matter there is from wherever you pick.

There'd be a lot of cosmology glory in proving that wrong. They'd put your name before Hubble's.

[0] - https://en.wikipedia.org/wiki/Cosmological_principle

Luck of the draw that they weren't lizard people on pangea, making that prediction.