“Remember: by June 10, 1861, when that first Confederate soldier (Pvt. Henry Wyatt of North Carolina), was killed at the Battle of Big Bethel, dozens of Union troops had already died, over 100 wounded and 500 captured and held as POWs.”
Well that tends to happen to troops involved in an invasion. The locals shoot back.
Confederate Pvt. Henry Wyatt from North Carolina was the first Confederate troop killed directly in battle, at Big Bethel on June 10, 1861.
But there was no Union "invasion" -- none -- before the Confederacy first provoked, then started and formally declared war on the United States, May 6, 1861.
Indeed, there was still no "invasion" until after Virginia voters ratified secession (May 23) and joined the Confederacy's already declared war on the United States.
But all during those months, in addition to seizing dozens of Federal properties (forts, ships, arsenals, mints, etc.), Confederates threatened Union troops & ships, fired at & damaged ships, wounded & killed troops -- in Fort Sumter, Fort Pickens, Baltimore, and Virginia (before secession) while around 500 Union troops were captured and held as POWs in Texas.
Point is: the Confederacy prosecuted vigorous war against the United States long before the Union did anything serious in response.