In 4 Nephi 1:48–49 we learned that Ammaron hid up all of the records in the Nephite year 320. Mormon tells us that it was about that time that Ammaron came to him. When Ammaron approached him, Mormon was 10 years old, therefore, he was born in the Nephite year 310 (or close thereto, depending upon how the months in the ten years lined up with the dates).
That Mormon was already being trained “after the manner of the learning of my people” at age ten suggests that he was in a royal family, though not necessarily the closest family to the ruler. We never see Mormon as the ruler of the nation, only as the General over all the armies.