First of all, we should note that cotton was not exactly the first big industry of the Industrial Revolution. It is more accurate to say that textiles (which included cotton but also included woolen fabrics) were the first major industry to make goods for consumers during the Industrial Revolution.
Textiles were one of the first major industries because of the fact that they are very basic to human life. Everyone needs clothes, so there is a clear demand for cloth. England’s population was also growing at the time, making even more demand than there had previously been. Food and shelter are the only other things as basic as clothing and those would have been much harder to industrialize.
In addition, industrializing the making of textiles was relatively simple from a technological point of view. The spinning of thread and the weaving of cloth are not terribly difficult to do by machine. Since textiles were very important and since they were not that hard to make by machine, they became the first big consumer industry of the Industrial Revolution.