Globes existed well before space travel. Mostly people would have thought of those as the closest approximation to viewing the Earth from space. You can see this in certain examples of special effects shots in scifi films, or in various artistic representations, or in educational films. For example, here's a screenshot from the original Star Trek show when they visited Earth: http://i.imgur.com/rcB1Ol0.jpg (from 1968). And here's an illustration from Chesley Bonestell: http://i.imgur.com/FxPFesg.jpg (from 1952).

One thing that's notable is the absence of extensive cloud cover. At any given time the Earth typically has 2/3 of its surface under cloud cover. This was somewhat known even in the 1960s through early imagery from weather satellites and other spacecraft. But perhaps because that imagery was grainy and in black and white it didn't really penetrate the public consciousness the way that later imagery such as "Earth rise" from Apollo 8 would. You can see that Bonestell did an excellent job of attempting realism but still missed the mark quite a bit in regards to clouds, adding only a few whispy clouds instead of the great whorls that are characteristic of the real thing.

As for how maps and globes were made so accurately even back to the 19th century. The answer is surveying techniques, most of them based on the principle of triangulation. From the 18th through 19th and 20th centuries a veritable army of surveyors pinpointed the locations of various geographic features across the globe. Bit by bit they knit together a mesh of surveying points that made it possible to use that data to create accurate maps of coastlines, political borders, mountain ranges, etc.