All traditional martial arts have a lineage. It is you, your teacher, your teacher's teacher, your teacher's teacher's teacher, and so on.
No one knows where martial arts originated from. Could be as early as when the first man made a fist to hit with and it evolved from that. So no, you can not trace a martial art back to it's origin. If you get far enough back it gets foggy. Stories are mixed in with reality and there is no way to tell which is what.
However a lot of times you can trace a martial art back to the beginning of a style. For example Karate styles can be traced back to Tode Sakugawa who passed it on to his student Bushi Matsumura. Tode Sakugawa lived from 1733-1815. There was martial art before that but who those people were is not clearly documented and the fighting style was supposedly crude.
Kung Fu too can be traced back to Shaolin in the sixth century AD and to the arrival of an Indian Buddhist monk, Bodhidarma, at the newly formed Shaolin Temple. Buddhism had been brought to China a few hundred years before that but Bodhidarma brought the new religion to the martial arts. Whether or not the monks at Shaolin were already versed in the martial arts and what exactly Bodhidarma taught them, is much disputed. However even before then there are records of martial arts dating back to Huang Di, the Yellow Emperor who was a general and propagated hand-to-hand martial arts' techniques in 2698 BC. Kung Fu is probably the one martial art that can actually be traced the furthest. We know about other martial arts the Greeks had for example but I don't think there is a continuous lineage. We know that Alexander the Great had a martial art which he got from Philip II of Macedonia, his father but there are holes in that lineage.