You'd have to define "subject". Are you talking about academic subjects, or tasks/fields of activity in general?
If the latter, you may be looking for the first profession - i.e. something that was important enough and required such knowledge and time to do well that it was worth making it a full time job/study.
A good contender for the first such task is that of flint knapping. This is taking us far enough back in time to be technically outside the scope of academic history (which is largely concerned with the study of written sources), but here goes.
Flints and other hard, flakeable minerals became the preferred materials for making tools across most of the populated world during the stone age. The earliest known example of crafted flint tools are "hand axes" from Olduvai gorge in modern day Tanzania, and date back approximately 2 000 000 years.
These early examples are very simple tools, but over the millennia they become more and more elaborate. In Eurasia the most advanced examples of crafted flints turn up in the neolithic ("younger stone age" - approx. 10000BCE-2000BCE). These are such complex creations that it has been estimated by modern experimental archaeologists that building up the knowledge and skill to make them would have been more or less a full time profession. The neolithic (or possibly even mesolithic) flint knapper would thus seem to qualify as the first known professional expert.
edit: Also, the oldest currently known stone tool is from Kenya, and dates back over 3 000 000 years.