Where the people who spoke this language lived, and when, is the field's longest running argument. The steppe hypothesis, placing them in the Pontic and Caspian grasslands in the fourth millennium BCE and associating them with the Yamnaya culture and with the horse and the wheeled vehicle, is the position most linguists and, since the ancient DNA work of the last decade, most archaeologists now hold. The Anatolian farming hypothesis, placing them earlier and further south, retains defenders.
The vocabulary itself is evidence. Reconstructed words for wheel, axle, yoke and wool imply a society that already had those things, which constrains the date, and the absence of a shared word for the sea points away from a coastal homeland.
This subject carries a bad history, and the atlas states it plainly. Nineteenth and twentieth century writers converted a language family into a race, invented an Aryan people, and used that construction to underwrite colonial hierarchy and, in Germany, genocide. Indo-European is a language family and nothing else, membership of it says nothing about ancestry or worth, and the word Aryan properly names only the self designation of the Indo-Iranian branch. The atlas records the linguistics and names the misuse rather than passing over it.