In medieval times, some people will be considered the founder of a dynasty but they clearly had parents, and their parents had parents and so on. Why do we consider a dynasty to start where it does or rather what’s considered the president for a dynasty to be “formed”? Is it a prestige thing? Or is the founder just as far back as the family can be traced?
"Dynasty" comes from the Greek dynasthai, which means "to be able" or "to have power." In other words, a dynasty is the ruling family.
So, the founder of a dynasty is the first one in that family to rule.
For example, the dynasty of the House of York starts when Edward Duke of York becomes Edward IV of England. The Tudor dynasty starts when Henry Tudor becomes Henry VII of England.
Even so, the first in a dynasty can sometimes be a tricky thing to nail down. For example, some claim Henry II of England to be the first of the Plantagenet dynasty, others consider him and his successors, Richard I and John, the Angevin dynasty and only start the Plantagenet with Henry III. This is made even more complicated by the fact that the Houses of Lancaster and York - important dynasties in and of themselves - are both cadet branches of the Plantagenet family. So, sometimes it's just a matter of convention and tradition.