Depending on your definition of sniping you could place it as early as the American Rebellion - units equipped with rifled guns were used to shoot important folks in the enemy formations (officers, artillerymen, etc). The British took this practice into the Napoleonic war (hands up who has read Sharpe) and both sides employed it in the war of 1812.
Since smokepole marksmen were mentioned: The Lone Marksman BTW, just reeived John Walter's Voices of Snipers which covers WW I & WW 2.
American rifleman Timothy Murphy famously killed (strictly speaking mortally wounded) British general Simon Fraser in one of the battles of the Saratoga campaign.
Paul Cheall of Fighting Through podcast reviews a sniper book from Casemate. 97 World War II Snipers - The Men, Their Guns, Their Story
Somewhere out there is a video a cousin sent me of a rifle that shot a bullet that actually turned a corner ?? I believe the projectile burst to the side and made a mess of the dude hiding around the corner?
Any idea where the energy came from to make it turn? Or was this a curving shot from the barrel? That might work.
It was some sort of rifle fired miniature missile, think 50 caliber size that spread shrapnel to the side at a set distance ?? this was 15-20 years ago. I'm not too sure of the accuracy but was interesting!
Paul Cheall at it again with part two of sniping: https://www.fightingthroughpodcast.co.uk/98-World-War-II-Snipers-Part-TWO/