It is true a sphere cannot be mapped to a flat plane. And you raise a fair point, if you could map a flat world with no distortion, where is said map?

If you look at the flat earth map all flat earthers use, the azimuthal equidistant projection, with lines of latitude & longitude to assist, you can see that the cells get wider and wider the further you move from the north pole. I must stress these are supposed to be SQUARES. That's the reason Australia looks twice as wide as it really is - because the map is distorted. And why is it distorted? Well, I'm sure you can come to that conclusion yourself.