It would be more accurate to say that a 3-sphere is a shape which might describe the topology of the Universe. But if it does, then that 3-sphere is extremely large, large enough that we can’t detect the curvature.
For a lower-dimensional analogy, the surface of the Earth is a 2-sphere. Note that there is no “edge of the Earth” that you can fall off of: In the same way, there is no “edge of the Universe” that one can pass to leave the Universe. But if you were limited to measurements made within, say, Ohio, it would be extremely difficult to tell that the surface of the Earth was a 2-sphere, because on that scale, the curvature is very small, almost indistinguishable from a flat plane. And if you further only had detailed measurements from downtown Columbus, plus a handful of much lower-quality measurements from a few other places in Ohio, then it would be very difficult indeed to tell that the Earth wasn’t flat.
That’s about where we stand with the Universe, except that the relative scales are actually much more extreme: We can do detailed measurements on the scale of, say, the Solar System, and much less informative measurements of more distant objects, and to within the limits of our measurements, so far as we can tell space is flat. It might not be: It might be spherical. But if so, then it’s so much larger than what we can measure that we can’t tell the difference.