For how long have deserts existed and which one would be the first to be created? I'm talking about arid, dry deserts, not the Antarctic or Arctic or any other icy deserts.
According to this Encyclopedia Britannica article, current desert regimes date back to no more than 65.5 million years:
The desert environments of the present are, in geologic terms, relatively recent in origin. They represent the most extreme result of the progressive cooling and consequent aridification of global climates during the Cenozoic Era (65.5 million years ago to the present), which also led to the development of savannas and scrublands in the less arid regions near the tropical and temperate margins of the developing deserts. It has been suggested that many typical modern desert plant families, particularly those with an Asian centre of diversity such as the chenopod and tamarisk families, first appeared in the Miocene (23 to 5.3 million years ago), evolving in the salty, drying environment of the disappearing Tethys Sea along what is now the Mediterranean–Central Asian axis.
Which would put the oldest of "modern" desert somewhere in the region of what later became North Africa or South Asia as the continents moved.
However, like John notes in the other answer, Britannica says "Deserts also probably existed much earlier, during former periods of global arid climate in the lee of mountain ranges that sheltered them from rain or in the centre of extensive continental regions. "
the first one would have been the entire planet soon after it formed (~4.4 billion years), the planet had to cool quite a bit before liquid water could exist. deserts basically predate all the other climes on earth.