Many of the others spoke languages with decidedly Dravidian and Uralic-Altaic connections (if not exactly roots). Indo-European languages arrived with outsiders long after post-glacial Europe had been completely resettled. Their languages come from an area of greater technological and agricultural prowess. Adopting those languages gave the European natives access to the intellectual background of the Indo-European societies.
That would included advanced bronze culture, then iron! Plus, they were already growing larger horses that could do real work and carry a mounted rider.
There's a very good case to make that the original Europeans came from Central Asia about 35,000 years ago during an interstadial (brief warm period) and then got trapped in the Western refugia for the next 20,000 years (this is on the French/Spanish border). The first folks out of the refugia were the Sa'ami who traveled East and North around the receding glacial lobe, and then West to America over the winter sea ice that then covered the North Atlantic.
The Europeans who went East from Central Asia became the Chinese, Jomon and other Far Eastern people.
The non-Europeans in the Middle-Eastern refugia became the Arabs, Hebrews, etc. The Europeans in the Mediterranean refugia became yet other people today variously identified as Southern Europeans.
Do not credit the Indo-Europeans, who were most likely as dark as the modern Persian upper-class, with being the first or original "white folks" in Europe.