[dullcrisp]

You can’t. The informal proof may not be very convincing but it’s that the torus has two circles that remain distinct no matter how you deform the space: the smaller and larger circles in this picture [1].

But on a sphere, every circle can be deformed to any other circle. If the torus were itself the deformation of a sphere, you’d be able to deform it the same way as the sphere to get one circle to the other.

Again though, the version of these objects that mathematicians study is formalized such that this is unambiguous.

[1] https://en.m.wikipedia.org/wiki/File:Tesseract_torus.png