The big issue, even for cosmologists today, is whether or not that primordial state contained some of the information needed for the appearance and development of the cosmos.
Cosmologists have done the equivalent of measuring our Universe's triangles by looking at a picture of the early Universe, and studying the spatial relationship between different points on that picture.
The second way to measure curvature is to measure the thing that causes space to curve in the first place: the density of energy and matter throughout the Universe. Which cosmologists have also measured.
Most cosmologists agree that the universe began with a gigantic explosion known as the Big Bang, but some believe that this event will inevitably lead to the end of the universe itself, known as the Big Rip.
The third option is that gravity is just right critical density is the cosmologists' term for it and that it will hold the universe together at just the right dimensions to allow things to go on indefinitely.
Interestingly, the man who found the answer to that question was a cosmologist who heartily despised the Big Bang as a theory and coined the term Big Bang sarcastically, as a way of mocking it.