The best proof of 'not a ball of the stated size' are visual. (or light doesn't travel in straight lines)

So, you take the govern-cement's website data on how far away certain light houses can be seen. Do the math, and find that they should be well over the horizon.

And, on a clear, still night, you can see these light houses from further.

Then their are the photographs you see, taken on a rare chance of clear, still days. Of cities that are so far, they should be over the horizon.

Today, there are many people taking such photos with IR cameras on the regular.

Other things, that are harder to prove, but are way more relevant is that there is too much land area below the equator. You measure points across the land mass... and they are longer than they should be measured on a globe.

One popular scientist who was confronted with this fact said "The earth is pear shaped"