yes, it is mind-blowing. Every time I think about it feels strange, it seems amazing, it is wonderful how we are capable of figuring this out and understanding the fact. And just by speed of light being constant, how our perception of reality changes, how our understanding reach to another level ,it is beautiful.
yes, there are many things in physics that seems strange, and special theory of relativity is one of those.

The direct evidence that we have that the Earth is spinning is the occurrence of day and night on the Earth, we can clearly see the setting and rising of the sun, dark and sunlight or change in the length of the shadow of an object under the sunlight. And first experimental evidence came from the French physicist Léon Foucault, which shows the coriolis effect (an apparent deflection of the path of an object in motion due to the rotation of the Earth) on a long heavy pendulum.