All deserts have one thing in common and that is that they are extremely dry. Most of the experts will agree that desert is an area that gets no more than 25 centimeters of precipitation each year. So, it is not a must that deserts have sand in them. There can be a desert that doesn't have much sand because by definition, deserts simply are extremely dry land with very little rain.
The sand may have been washed in by rivers or streams from distant and less dry times. So, the sand arrived there most probably before the land became a desert region. Then, as soon as the area becomes arid, lack of vegetation or water to keep the soil in place. The winds blow over the region and takes away the soil and leaves just the sand.