Wow. Just to put that in perspective, it was a desert when North America was still joined to Europe, India wasn't and Australia was an Antarctic appendage:
Then the American Southwest was grasslands, until gold rush and westward expansion including cattle and sheep, resulting in overgrazing and irreversible changes.
The Gobi was widely inhabited in prehistoric times. People arrived and wham! desert. Its still expanding today, one of the fastest-growing deserts in the world. Because, people.
The Namib is indeed old. Its also almost the smallest desert - #25 on a list of 27 worldwide. So lets grant an exception there.
Also roads going through deserts does not prove much since they could just connect oasis or move goods across the desert without people living within it.
The Sahara itself also is fairly old[0]. Of course its total extent is variable and subject to natural and man-made climate change and other human influence. But there is a huge difference between human activity creating a desert and influencing its extent or aridity.
Most deserts are naturally created through the rain shadow[1] and other precipitation-reducing effects of geographic features.
[0] https://www.researchgate.net/profile/Zhongshi_Zhang/publicat... [1] https://en.wikipedia.org/wiki/Rain_shadow