We can’t see all of the Earth at once, and we had really good maps of the whole world even before satellites.
We can look into space in all directions with pretty much nothing getting in our way.* Map all of the stars (direction and distance) in every direction and you get a Milky Way map.
The semi-automated Gaia Catalogue has mapped around 2 billion stars, out of the estimated 100 billion in total. That’s still enough to have a pretty detailed map.
*The galactic center is too dense with stars to see *through*, so we have a blind spot there.
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