Tough question! There's lots of room for more discussion, but thought you would be interested in some previous posts
The question
When was the first properly accurate map made? - /u/khosikulu suggests that 'no map is ever really accurate'
Who created the first complete accurate map of the world and when? - /u/restricteddata and /u/khosikulu kick the question around some more
Some proposed answers
How early did mankind first have an accurate map of the entire globe? - /u/Capt_Blackadder suggests 1808 with caveats
When was the first time in history that a [relatively] detailed and accurate map of the entire earth existed? - /u/snackburros makes a few nominations
When we first saw the earth from high altitude did we have to make any major changes to our world maps? - a lively discussion on some recent additions / corrections
cartography
and see more in the FAQ History of Cartography