They have seen this confirmed in many ways. among them, are by taking samples off the ocean floor of the Atlantic near the coast of Morocco.
they can date the layers of mud going back many thousands of years. what they see is that roughly before 3500 BC the mud is thick with pollen as you would see coming off North Africa from a green grassy world.
The newer sediments are nearly devoid of pollen as you would see coming off North Africa from the desert.
The transition happened fairly quickly—within just 100 years.