Antarctica was the last continent to be discovered, and the first confirmed landfall was on January 24, 1895. However, most discussions of "early" world maps seem to peter out well before that, such as this Wikipedia article which only goes up to 1630.
The situation is muddied even more by the fact that Antarctica (known then as Terra Australis) appeared on many world maps before it was even discovered, such as this 1570 map. However, this is based on arguments from legends and various erroneous information, rather than on any actual evidence.
Surely after humanity first set foot on the "last continent", it wasn't long before they started mapping the real shape of it. When was the first map produced based on this real information (regardless of whether it was actually "accurate" in the era before we had artificial satellite technology etc)?
This question is made even more important by the fact that a world map incorporating this shape would be "largely" complete, although world maps would arguably not really be complete (in terms of approximate landmass shapes) until the first whole maps of Severnaya Zemlya were completed in 1932.