Wordorigins.org

Hotshot, meaning a brash, flashy, and successful fellow, is an Americanism dating to 1927. From J. Frank Dobie’s Texas And Southwestern Lore from that year:

Men who are either slow or lazy are given such names as..."Hot Shot”..."Lightning,"...and “Speedy.”

There is an older British sense of the term meaning an undisciplined troublemaker. In 1600 playwright John Marston wrote:

By gor me am a hot shot.

And in 1604 Thomas Middleton wrote in Father Hubbards Tales:

To the wars I betook me, ranked myself amongst desperate hot shots.

But this older sense isn’t recorded in American usage and is probably not the source of the American term. Ultimately, both the British and the American usages come from the literal meaning of a bullet that is hot from firing.

It is commonly stated that this is term is naval in origin and refers to the practice of using heated shot to set ships afire. This is almost certainly not the case. None of the early figurative uses are from naval sources or contexts. And while naval texts can be found that use the words “hot shot,” these are invariably in a quite literal sense, not a metaphorical one.

(Sources: Historical Dictionary of American Slang; Oxford English Dictionary, 2nd Edition)