I've been told by some that the CSA's departure from the Union was peaceful, and that it was the Northern incursion into the South that sparked hostilities. Is there any truth to this?
No. The war began because southern troops attacked the union garrison at Fort Sumter in Charleston harbor.
It should be noted that the union garrison had been in Charleston harbor since before the declaration of secession by South Carolina in Dec. 1860. The Union commander of the troops in the smaller Fort Moultrie moved his forces, along with some of his cannon to the more defensible, but still as yet incomplete Fort Sumter six days later on Dec. 26, 1861. By January, South Carolina's government had demanded that the Union troops evacuate the fort, but they refused. A supply ship sent in early January was fired upon by Confederate troops. So a stalemate ensured for several months with the troops in Fort Sumter running ever lower in supplies, while refusing to leave.
Lincoln was inaugurated in March 1861, and immediately ordered a resupply convoy to stock the Fort, which by this point was running very low on supplies, scheduled to completely run out by April 15. The supply convoy arrived on April 11, but by that point it was almost too late. The main fort was attacked early the next morning with a full on Confederate artillery barrage thus starting the war.
So like many lies told by neo-confederates and confederate apologists, what your friend says does have a grain of truth inside the sea of falsehood. Yes, one could argue that it was "northern incursion" - in the form of the resupply convoy sent by the United States to support US troops who were occupying a US government built and maintained naval base, but arguing that would be intellectually dishonest, to say the least. Hostilities began because the South attacked the North.
Bonus points: You can go back to your apologist friend and let him/her know that the war was also, entirely, about slavery. Since he won't believe you, direct him to the South Carolina Declaration of Secession which clearly lays out that protection of slavery was, in fact, the reason.
Given that the American Civil War started with the Confederate attack on Fort Sumter, it's a little difficult to blame on northern aggression. Unless refusing to evacuate a fort constitutes an aggressive act.