We can measure that the Universe is homogeneous and isotropic on sufficiently large scales (it is according to the measurements). We can also measure the 'flatn

We can measure that the Universe is homogeneous and isotropic on sufficiently large scales (it is according to the measurements). We can also measure the 'flatness' of the Universe (it is very likely to be flat, according to measurements). I don't know the details, but I was told that with these assumptions, proving that the Universe is infinite is only a matter of mathematics.