Read about measurements of the flatness of space. To the precision we're capable of measuring, it appears completely flat.

Then picture us as ants on a surface that appears flat as far as we can see. Are we on an infinitely sized surface? Either we are, or it's a sphere but the surface is curved but so slightly that it appears flat. This implies the sphere is much bigger than our observable area.

Note, we're assuming the universe doesn't just end we arbitrary boundaries. It either is infinite or it curves back on itself.