It's been over a decade since my cosmology class, so forgive any errors, but isn't there a constant that describes the curvature of the universe [1], which so far has been calculated as "flat"? That's not to say we'll ever truly know, since you need infinite precision to rule out hyperbolic or spherical geometry, but in a flat universe, how can you have toroidal geometry?
Per [2]:
> The actual value for critical density value is measured as ρcritical = 9.47×10−27 kg m−3. From these values, within experimental error, the universe seems to be flat.
It’s actually no problem mathematically to have toroidal topology and flat geometry. (The classic Asteroids video game, where your ship can go off the top of the screen and come in at the bottom, or similarly with the left and right edges, is an example of a flat 2D space with the topology of a torus.)
Per [2]:
> The actual value for critical density value is measured as ρcritical = 9.47×10−27 kg m−3. From these values, within experimental error, the universe seems to be flat.
[1] - https://en.m.wikipedia.org/wiki/Friedmann_equations#Density_...
[2] - https://en.m.wikipedia.org/wiki/Shape_of_the_universe