In the late 1800's, Dr. Jigaro Kano invented the sport of Judo and invented a reinforced Jacket for Judoka to wear so the students' throwing techniques would not tear their clothes off. This uniform became modified over the years until we have our current uniforms. For many centuries, the belt did not signify rank. Again, it was Dr. Kano, the founder of Judo, who introduced the use of different belt colors to denote ranks. He did this to make it easy to identify different ranks for competition.
Different systems use different colors.
Most Chinese martial arts don't use belts but use sashes instead. In Japanese martial arts, the belt was used to keep the jacket closed and was white. With years of practice, the belt would become soiled and stained and would eventually turn black. The colors used in the Korean martial arts are based on the colored robes worn by the different classes of royalty in the ancient Kingdom of Silla. After two to three months, you should be ready for your first rank promotion.