Get some blu tac, two cocktail sticks and a piece of string 30 cm long and a large mixing bowl.
Turn the mixing bowl over and put part of the blu tac on one part of the curved side. The western hemisphere if you will.
Push a cocktail stick into the blu tac so it's perpendicular to the surface of the bowl.
Use your 30cm string to measure from the base of the cocktail stick to the 'eastern hemisphere of the bowl'. Stick blu tac to the bowl. Insert stick into the blu tac perpendicular to the bowl.
Next measure 1 inch up a cocktail stick, and extend the string from one cocktail stick to the other, you'll see that the string is slightly short. Do the same from tip to tip and you'll see that it's shorter again.
This is a primary school experiment.
I know you struggle with scale, but obviously if this was scaled up to global size those sticks would be thousands of miles high and the string thousands of miles long.
But the experiment would work on a small scale or a large scale.
It's fairly easy to comprehend how/why curvature would need to be accounted for when building a large suspension bridge. The foot of the towers are marginally closer together than where the road deck would sit.