Well, we can't verify the shape of our universe, but we can make good guesses. And in Ralph Rotten's defense, looking at structures inside the universe does gives us some clues to the shape of a larger system, with limitations ofc.
For example, from looking at our solar system and planets within it, we observed the interaction between gravity and angular momentum, or spin. From these observations and calculated approximations of mass and density of our galaxy both towards the galaxy center and away, we made a good guess of the shape of the Milky Way. We've never seen the entirety of our galaxy ever, but we can be pretty confident about our guess when there is a plethora of other galaxies to verify our models against and everything operates in 4 neat dimensions.
That being said, the Universe may or may not operate on the same principles as the things within it. For example, if the Cosmological Principle holds true and we use the same logic as before, we should be able to say that the universe is relatively close in size in each of its 3 spatial dimensions and that the Universe is not spinning, because matter is relatively distributed and it should not be the case if the Universe is spinning.
But if you think about it for another few minutes, you would realize this idea breaks in quite a few places. I'll leave finding those places to you as I found it quite fun to think about.
However, there are still pieces we can gleam from our observations that are likely to be useful.
What our current theories on the shape of the universe stem from stuff in Einstein's GR, the space-time curvature models portion of it to be more precise.
This link pretty much tries to answer-but-not-answer your exact same question:
https://starchild.gsfc.nasa.gov/docs/StarChild/questions/question35.html
The overall answer is contingent on us getting a bunch of other things about our universe right, such as dimensionality, rate of change in the rate of expansion, etc.
